Today there are in arxiv two articles that look really great.
The firs (in the order that arxiv gives to them) is from Samir D. Mathur: Effective information loss outside the horizon.
It argues that there is no loss of information inside a black hole because he information simply doesn't go inside the black hole. The abstract explains it more carefully:
If a system falls through a black hole horizon, then its information is lost to an observer at infinity. But we argue that the {\it accessible} information is lost {\it before} the horizon is crossed. The temperature of the hole limits information carrying signals from a system that has fallen too close to the horizon. Extremal holes have T=0, but there is a minimum energy required to emit a quantum in the short proper time left before the horizon is crossed. If we attempt to bring the system back to infinity for observation, then acceleration radiation destroys the information. All three considerations give a critical distance from the horizon $d\sim \sqrt{r_H\over \Delta E}$, where $r_H$ is the horizon radius and $\Delta E$ is the energy scale characterizing the system. For systems in string theory where we pack information as densely as possible, this acceleration constraint is found to have a geometric interpretation. These estimates suggest that in theories of gravity we should measure information not as a quantity contained inside a given system, but in terms of how much of that information can be reliably accessed by another observer.
The other article is written by Maldacena: Einstein Gravity from Conformal Gravity.
The abstract is:
We show that that four dimensional conformal gravity plus a simple Neumann boundary condition can be used to get the semiclassical (or tree level) wavefunction of the universe of four dimensional asymptotically de-Sitter or Euclidean anti-de Sitter spacetimes. This simple Neumann boundary condition selects the Einstein solution out of the more numerous solutions of conformal gravity. It thus removes the ghosts of conformal gravity from this computation. In the case of a five dimensional pure gravity theory with a positive cosmological constant we show that the late time superhorizon tree level probability measure, $|\Psi [ g ]|^2$, for its four dimensional spatial slices is given by the action of Euclidean four dimensional conformal gravity.">We show that that four dimensional conformal gravity plus a simple Neumann boundary condition can be used to get the semiclassical (or tree level) wavefunction of the universe of four dimensional asymptotically de-Sitter or Euclidean anti-de Sitter spacetimes. This simple Neumann boundary condition selects the Einstein solution out of the more numerous solutions of conformal gravity. It thus removes the ghosts of conformal gravity from this computation.
In the case of a five dimensional pure gravity theory with a positive cosmological constant we show that the late time superhorizon tree level probability measure, $|\Psi [ g ]|^2$, for its four dimensional spatial slices is given by the action of Euclidean four dimensional conformal gravity.
Unfortunately until the next Friday I am going to be very busy and I badly will have time to read them carefully those days so I can't say too much more about them. I suppose that (at least) Lubos will talk about them so I will read its report before I can read them myself. I write this entry partially to recommend the articles to however could be interested and also to keep a link to them so I could later have a quick access to them from wherever I want.
Update: Well, at last I had no patient and read the first article (after all is a brief one, only 7 pages). I have a mixed filling about it. The author computes a few things related to the fall of a body towards an event horizon. Firstly he does for an Schwarschild one.
There he considers two cases. The first in the free fall. In that case the last light (containing the info about the object) is emitted, because of the red-shift at a frequency bellow the Hawking temperature and so it can't be differentiated from this and he concludes that we actually don't have the information about that object.
The second case is when an observer at infinity holds the infalling object until the last time. In that case it is the unrhu radiation associated to the acceleration of an object at rest respect to a gravitational field which is responsible for a dissipation of the information of the object when it finally is released and cross the horizont.
Later he calculates similar things for a Reissner-Nordstöm like black hole and he finds that somewhat different mechanism operate in order to get similar qualitative and quantitative results.
In the last part he does calculations using string theory and the fuzzball paradigm for black holes (where the notion of event horizon is replaced by an stringy construction). Still he finds equivalent results.
Certainly the fact that many different calculations lead to a similar result is appealing. But still I don't see clear the whole subject. I think that at best he would be saying that the lost of information happens before the horizon (or its fuzzball "equivalent") so the problem of lost of unitarity remains (and even we could say that is getting worst because it happens in a region causally connected with the outsider observer). But the whole thing is that one could think that a priory we could think that if the outside of the black hole is clean of other infalling matter (other that the actual object under study) we could argue that if we know the state of the object at infinity we can apply the laws of quantum mechanics to know t's state when it is falling (eve it we can't actually do a measure to be sure that nothing has perturbed our object). That contrast the case of the object that falls behind the horizon when we have no idea of which it's final state would be because we don't know the laws of quantum gravity near the singularity. Well, I am ware that this last objection is somewhat wrong because the key point of the lost of information is the horizon and not the singularity but I have no more time just now to see what point I am missing. I'll realize it for sure later, but I don't promise to write it here soon. But keep calm, for sure Lubos will write about it sooner or later and will clarify the relevant points ;).
Showing posts with label black holes. Show all posts
Showing posts with label black holes. Show all posts
Monday, May 30, 2011
Tuesday, April 19, 2011
Can we see inside black holes?
The last week there was an article that was commented in the arxiv blog: Planets Could Orbit Singularities Inside Black Holes.
The blog entry discuses this article: Is there life inside black holes?.
The article is a pure classical relativity article. It study the possibility of stable orbits for planets inside a black hole, in particular in a Kerr-Newman black hole, that is, a rotting charged black hole. The classical geometry of a Kerr-Newman black hole is described by it's Penrose diagram:
The essential aspect of the K-N black holes for the work of that people is the presence of the inner horizon (a Cauchy horizon). In a non rotating black hole, described by the Schwarschild metric, once he cross the event horizon the radial coordinate changes it sign acquiring a time sign. That means that one must go in the direction of decreasing radius until one finds the central point-like singularity. A common interpretation of that geometry is to say that inside the black hole the space itself is falling toward the centre at the speed of light and it drags averything with it.
In the K-N case things are somewhat richer. In addition to the outer event horizon there is an inner cauchy horizon. When the black holes spins faster and faster (or when the charge of the black hole increases) both horizons get nearest and nearest until, ultimately, they would converge and it would become an extreme black hole.Beyond that one would have a naked singularity but it is thought that such a possibility should be ruled out.
well, as a I said te key point was the cuchy horizon. AS you can read in the linked wikipedia article a Cauchy Horizon is a boundary for the validity of a well posed Cauchy problem in partial differential equations. It can be shown that light (or whatever wave) crossing the horizon gets an infinite blue-shift. That means that it's energy-momentum tensor diverges. The implication of it would be that the back-reaction would destroy the Cauchy horizon once a particle cross it. Still one could get an stable Cauchy horizon if one throws in it exotic matter violating the AWEC (average weak energy condition) well known for people working in wormholes.
The reason why the cauchy horizon is important is because once it is crossed the radial coordinate becomes once again space like. That opens the possibility of the existence of stable orbits inside the black hole. In previous articles, cited by the author, it was shown the existence of that orbits for Reisner-Nordstöm (charged) and Kerr (rotating) black holes. The present article generalizes the results to the general case. In the article considerations are hold about the tidal forces, sizes, radiation rates and they conclude that in a galaxy centre sized black hole a planet could do an stable orbit around the singularity and hold life.
Well, this is the content of the article. As I have explained it is worked in the ansatz of the validity of classical relativity inside a black hole. Also it depends strongly in the stability of the cauchy horizon that can't be got without exotic matter. Note: the author doesn't mention that point about exotic matter although he is aware of the fact that cauchy horizons are not stable. Without exotic matter the whole paper is of a purely academic interest even if one accepts that classical general relativity is accurate to describe black holes inners.
Of course there are a lot of people who don't like classical GR for doing so. In string theory there are many alternative descriptions. On one side one has the correspondence principle of black holes (due to t' hooft and Suskind) that says that an observer falling into a black hole will not be able to notice when he has crossed the even horizon. That means that the physic he sees is must be equal that the physics seen by an outside observer. The reason of the introduction of that principle is the intent of saving unitarity in the presence of Hawking radiation. The actual reasoning is made not classically but for the Hilbert space of a quantum theory as seen but inner and outer observers.
Another string theory inspired viewpoint is described in a classical article by Maldacena: D-brane Approach to Black Hole Quantum Mechanics . In the last part of that article, after calculating the Beckenstein-Hawking entropy, Maldacena Suggest a view where black holes inners and Hawking radiation is described in terms of D-branes. I am not aware if that suggestion has been further developed. I have made a partial search for "hawking radiation in string theory" but I haven't found too much. In fact, beyond that Maldacena article, I found only an approach written some years before using a very aproximative description.
Another paradigm for black hole inners in the string literature would be the fuzzball approach of Mahupart (or maybe Mithur I am not sure at this point and have not time to do a search just now).
Well, that variety of viewpoints, not very compatible among them, for the black hole inner is disappointing. Even in the simpler case of the general relativity viewpoint is disappointing the possibility of the existence of stable structures (maybe planets of an advanced alien civilization, maybe a much more prosaic rings of dust) existing inside the black hole hidden for us from the event horizon.
But, wait! The title of the post wonders about the possibility of seeing inside the black hole. Of course classically it is impossible because of the very meaning of "event horizon". But when quantum mechanics enter the game thing could change. Of course the key would be Hawking radiation. The semiclassical theory says that the radiation must be purely thermodynamic so we can't get any info from it. But if unitarity is conserved the Hawking radiation can't be purely thermodynamic and it must have some structure that stores all the structure of the matter that formed the black hole and that has fallen inside it after it's formation. Possibly it will also have some information about the inner structure of the black hole. Obviously to get that info is very difficult in practice. The usual analogy is to say that one could reconstruct, in principle, the form of a living object from the ashes that are produced when it is burn.
But if we are a little least ambitious maybe we could actually get some partial information. Maybe we could design some easy mental experiment in which throwing into the black hole some specific kind of matter in some specific way we could analyse the Hawking radiation related to it to get some information of the inside of the horizon. That would actually be very cool because it would give an experimental way to distinguish the competing descriptions of the black hole inner.
Of course I actually don't know the details of how this could be done (only a very vague ideas that probably will not work). But maybe something on this purpose is already made and a kind reader would give me the references ;).
The blog entry discuses this article: Is there life inside black holes?.
The article is a pure classical relativity article. It study the possibility of stable orbits for planets inside a black hole, in particular in a Kerr-Newman black hole, that is, a rotting charged black hole. The classical geometry of a Kerr-Newman black hole is described by it's Penrose diagram:
The essential aspect of the K-N black holes for the work of that people is the presence of the inner horizon (a Cauchy horizon). In a non rotating black hole, described by the Schwarschild metric, once he cross the event horizon the radial coordinate changes it sign acquiring a time sign. That means that one must go in the direction of decreasing radius until one finds the central point-like singularity. A common interpretation of that geometry is to say that inside the black hole the space itself is falling toward the centre at the speed of light and it drags averything with it.
In the K-N case things are somewhat richer. In addition to the outer event horizon there is an inner cauchy horizon. When the black holes spins faster and faster (or when the charge of the black hole increases) both horizons get nearest and nearest until, ultimately, they would converge and it would become an extreme black hole.Beyond that one would have a naked singularity but it is thought that such a possibility should be ruled out.
well, as a I said te key point was the cuchy horizon. AS you can read in the linked wikipedia article a Cauchy Horizon is a boundary for the validity of a well posed Cauchy problem in partial differential equations. It can be shown that light (or whatever wave) crossing the horizon gets an infinite blue-shift. That means that it's energy-momentum tensor diverges. The implication of it would be that the back-reaction would destroy the Cauchy horizon once a particle cross it. Still one could get an stable Cauchy horizon if one throws in it exotic matter violating the AWEC (average weak energy condition) well known for people working in wormholes.
The reason why the cauchy horizon is important is because once it is crossed the radial coordinate becomes once again space like. That opens the possibility of the existence of stable orbits inside the black hole. In previous articles, cited by the author, it was shown the existence of that orbits for Reisner-Nordstöm (charged) and Kerr (rotating) black holes. The present article generalizes the results to the general case. In the article considerations are hold about the tidal forces, sizes, radiation rates and they conclude that in a galaxy centre sized black hole a planet could do an stable orbit around the singularity and hold life.
Well, this is the content of the article. As I have explained it is worked in the ansatz of the validity of classical relativity inside a black hole. Also it depends strongly in the stability of the cauchy horizon that can't be got without exotic matter. Note: the author doesn't mention that point about exotic matter although he is aware of the fact that cauchy horizons are not stable. Without exotic matter the whole paper is of a purely academic interest even if one accepts that classical general relativity is accurate to describe black holes inners.
Of course there are a lot of people who don't like classical GR for doing so. In string theory there are many alternative descriptions. On one side one has the correspondence principle of black holes (due to t' hooft and Suskind) that says that an observer falling into a black hole will not be able to notice when he has crossed the even horizon. That means that the physic he sees is must be equal that the physics seen by an outside observer. The reason of the introduction of that principle is the intent of saving unitarity in the presence of Hawking radiation. The actual reasoning is made not classically but for the Hilbert space of a quantum theory as seen but inner and outer observers.
Another string theory inspired viewpoint is described in a classical article by Maldacena: D-brane Approach to Black Hole Quantum Mechanics . In the last part of that article, after calculating the Beckenstein-Hawking entropy, Maldacena Suggest a view where black holes inners and Hawking radiation is described in terms of D-branes. I am not aware if that suggestion has been further developed. I have made a partial search for "hawking radiation in string theory" but I haven't found too much. In fact, beyond that Maldacena article, I found only an approach written some years before using a very aproximative description.
Another paradigm for black hole inners in the string literature would be the fuzzball approach of Mahupart (or maybe Mithur I am not sure at this point and have not time to do a search just now).
Well, that variety of viewpoints, not very compatible among them, for the black hole inner is disappointing. Even in the simpler case of the general relativity viewpoint is disappointing the possibility of the existence of stable structures (maybe planets of an advanced alien civilization, maybe a much more prosaic rings of dust) existing inside the black hole hidden for us from the event horizon.
But, wait! The title of the post wonders about the possibility of seeing inside the black hole. Of course classically it is impossible because of the very meaning of "event horizon". But when quantum mechanics enter the game thing could change. Of course the key would be Hawking radiation. The semiclassical theory says that the radiation must be purely thermodynamic so we can't get any info from it. But if unitarity is conserved the Hawking radiation can't be purely thermodynamic and it must have some structure that stores all the structure of the matter that formed the black hole and that has fallen inside it after it's formation. Possibly it will also have some information about the inner structure of the black hole. Obviously to get that info is very difficult in practice. The usual analogy is to say that one could reconstruct, in principle, the form of a living object from the ashes that are produced when it is burn.
But if we are a little least ambitious maybe we could actually get some partial information. Maybe we could design some easy mental experiment in which throwing into the black hole some specific kind of matter in some specific way we could analyse the Hawking radiation related to it to get some information of the inside of the horizon. That would actually be very cool because it would give an experimental way to distinguish the competing descriptions of the black hole inner.
Of course I actually don't know the details of how this could be done (only a very vague ideas that probably will not work). But maybe something on this purpose is already made and a kind reader would give me the references ;).
Friday, April 09, 2010
Á guide for anonymous LHC backholics
A few days ago it was published on arxiv the following paper: Black hole/string ball production, possibly at LHC
I am busy reading any, many things nowadays and I couldn't read it immediately - despite of it's few number of pages - but today, at last, I read it.
The main interest of the papers is that it makes a quick review of the ideas that lead to the proposal of black hole creation on the LHC and to it's characteristics. Most interestingly still, it gives references to the relevant literature.
One of the focus +of the paper is the way on which the Hawking radiation is expected to behave. It is said that the first expectation was that most of the radiation would be send t Kaluza-Klein models of the gaviton that scape to the bulk. In particular a paper stating that was: A Model for High Energy Scattering in Quantum Gravity (note that the article treats other aspects as well).
Later it was argued that instead there would be a lot of hawking emission into brane particles: Black Holes Radiate Mainly on the Brane . In this paper, like in the others, the treatment is semiclassical. No construction of black out of D-branes is used. Neither Hawking radiation is described by string theory objects. Such descriptions exist, to a certain extent, but are not developed enough to use them in this contexts. In fat an analytic description of a black hole in braneworlds is inexistent even in classical gravity and some reasonable approximations have to be made. This approximations are valid for small black holes whose size is much smaller than the length of the extra dimension.
The amount of radiation send to the bulk or to the brane is important. If all the radiation is send to the brane no Hawking radiation would be observed in the LHC.
Well. I think that this article is citing mainly orthodox string theory friendly papers. Be aware that other people argue that a microcanonical statistical ensemble would be necessary. In that assumptions the lifetime of the back holes could be large enough to leave the detectors (but still there woulld, of course, no danger of earth swallowing black holes).
The theme of black hole emission has behind it a lot of publications and many, many, possibilities have been conjectured. One of that is the possibility of formation of a "cromosphere" or an "electrosphere". By that it is understood that the hawking radiation reorganizes into a permanent orbiting matter that obstruct the rest of the outgoing radiation to some extent. A recent paper in arxiv (sorry, I have no time to search the reference now) argues against it.
Also there have been more exotic ideas. For example Louis Crane abrogate for the possibility of creating black holes by collapsing large clouds of dust, of a few tons, by means of implosions. He argues that the resulting black hole would emit in supersymmetric modes and that the radiation could be modulated to use the black hole as a device to impulsate spaceships able to go into other solar systems. I have discussed this, and the one of microcanonical ensembles, possibility in my other blog. You can search there for them (if you speak Spanish).
As the readers could guess some of the suggestions in the literature have more wide acceptation, possible with very good reasons, that others. And, except for the Louis Crane idea, all depends on braneworld sceneries. Recently there was an article in arxiv that gives a wide sight into realizations of that models into full string theory. When I would have read it I'll try to summarize some of the proposals here.
UPDATE: Today Lubos has commented about an article treating black holes: Kerr black hole: the CFT entropy works for all M,J. Of course it is worth reading.
I am busy reading any, many things nowadays and I couldn't read it immediately - despite of it's few number of pages - but today, at last, I read it.
The main interest of the papers is that it makes a quick review of the ideas that lead to the proposal of black hole creation on the LHC and to it's characteristics. Most interestingly still, it gives references to the relevant literature.
One of the focus +of the paper is the way on which the Hawking radiation is expected to behave. It is said that the first expectation was that most of the radiation would be send t Kaluza-Klein models of the gaviton that scape to the bulk. In particular a paper stating that was: A Model for High Energy Scattering in Quantum Gravity (note that the article treats other aspects as well).
Later it was argued that instead there would be a lot of hawking emission into brane particles: Black Holes Radiate Mainly on the Brane . In this paper, like in the others, the treatment is semiclassical. No construction of black out of D-branes is used. Neither Hawking radiation is described by string theory objects. Such descriptions exist, to a certain extent, but are not developed enough to use them in this contexts. In fat an analytic description of a black hole in braneworlds is inexistent even in classical gravity and some reasonable approximations have to be made. This approximations are valid for small black holes whose size is much smaller than the length of the extra dimension.
The amount of radiation send to the bulk or to the brane is important. If all the radiation is send to the brane no Hawking radiation would be observed in the LHC.
Well. I think that this article is citing mainly orthodox string theory friendly papers. Be aware that other people argue that a microcanonical statistical ensemble would be necessary. In that assumptions the lifetime of the back holes could be large enough to leave the detectors (but still there woulld, of course, no danger of earth swallowing black holes).
The theme of black hole emission has behind it a lot of publications and many, many, possibilities have been conjectured. One of that is the possibility of formation of a "cromosphere" or an "electrosphere". By that it is understood that the hawking radiation reorganizes into a permanent orbiting matter that obstruct the rest of the outgoing radiation to some extent. A recent paper in arxiv (sorry, I have no time to search the reference now) argues against it.
Also there have been more exotic ideas. For example Louis Crane abrogate for the possibility of creating black holes by collapsing large clouds of dust, of a few tons, by means of implosions. He argues that the resulting black hole would emit in supersymmetric modes and that the radiation could be modulated to use the black hole as a device to impulsate spaceships able to go into other solar systems. I have discussed this, and the one of microcanonical ensembles, possibility in my other blog. You can search there for them (if you speak Spanish).
As the readers could guess some of the suggestions in the literature have more wide acceptation, possible with very good reasons, that others. And, except for the Louis Crane idea, all depends on braneworld sceneries. Recently there was an article in arxiv that gives a wide sight into realizations of that models into full string theory. When I would have read it I'll try to summarize some of the proposals here.
UPDATE: Today Lubos has commented about an article treating black holes: Kerr black hole: the CFT entropy works for all M,J. Of course it is worth reading.
Wednesday, April 22, 2009
Naked singularities
This month, April 2009, the Spanish edition of Scientific American(investigación y ciencia)has an article about naked singularities (the English version was dated on February).
The author, Pankaj S. Joshi, seems to be an total expert in the subject (a common issue in Scientific American)and has a recent book- from 2008- about the particular,
Gravitational Collapse and Spacetime Singularities.
I didn´t read the book, but I found the article interesting so I searched in wikipedia and some of the papers linked there. I´ll try to explain some of the aspects now.
In general relativity there are two well known places where singularities appear, black holes and cosmology. The most naive way of thinking/defining singularities is to characterise them as points where the metric (or curvature) of space-time becomes infinite. According to that the event horizon of a Schwarschild black hole would be a singularity. It was realized that that infinity was due to a bad choice of coordinates. In that solution the centrer of the black hole, the R=0 point, also get an infinity value and this can´t be overcome by any other choice of coordinates so it is a genuine singularity.
As far as we like to have coordinate free definitions there is more technical definition, a singularity is defined to be one which contains geodesics which cannot be extended in a smooth manner. The end of such a geodesic is considered to be the singularity. That definition is useful to probe theorems (as did Penrose and Hawkings in the 70´s) about how singularities can´t be avoided in classical general relativity in cosmological sceneries. It also permit to make a diferentiation about coordinate singularities, the ones I talked before, related to black holes, and what are known as conical singularities, related to things such as cosmic strings. A conical singularity occurs when there is a point where the limit of every diffeomorphism invariant quantity is finite. In which case, spacetime is not smooth at the point of the limit itself. Thus, spacetime looks like a cone around this point, where the singularity is located at the tip of the cone. The metric can be finite everywhere if a suitable coordinate system is used.
The S.A article treats about singularities associated to gravitational collapse. There exists what is known like the cosmic censorship conjecture (or hypothesis) , own to Roger Penrose, which states that there are not naked singularities. That is, every singularity must be hidden behind an event horizon and cant be seen from the outside. It has the status of conjecture because it hasn´t be proved in a rigorous way under physically reasonable assumptions. In fact it hasn´t even stated in a mathemathical rigorous way.
The article, obviously, try to answer the conjecture in the negative. Before describing it's arguments I´ll talk about an aspect closely related to the CCC. If one examines the solutions for rotating black holes (Kerr solution) one sees that if is allowed that J, the angular momentum is greater than the mass M of the black hole, that is J/M>1 a naked singularity (a ringed shaped one) appears. A similar thing goes for charged (electric of whatever associated to U(1) gauge symmetry)black hole solutions (Reissner-Nordstom black holes) where a naked singularity appears if the charge, Q, is greater than the mass of the b-h, i.e., Q/M>1. It is commonly assumed that the CCC holds and the case where the equality would arise are called extremal black holes. The possibility of a reverse, negative, sign in the above expressions is not even contemplated in most theoretical considerations.
That´s a reason why I was somewhat surprised when I read the article and saw that in fact when one makes actual calculations, in classical general relativity, of how gravitational collapse behaves when some oversimplifying assumptions about the state of the star are neglected naked singularities actually are shown to be possible.
If the star is perfectly spherically symmetric and of uniform density everything is o.k and the black hole is formed. But relaxing one of the assumptions separately(or both at once) it can be shown that naked singularities actually appear.
Intuitively the reason is, for the case of non uniform density, that it can happen that the rate of accretion into the centre is never fast enough to actually form an even horizon and a central, unique, singularity appears. In the case of non sphericity it is shown that the collapse is neither spheric so the mass is concentrated in two points that become singularities at the end of the collapse avoiding the formation of the event horizon because of the oblong shape of the infalling matter that forbids the concentration of enough mass inside the Schwarschild radius.
Once that this facts are established one can wonder about how realistic and stable are. After all they mean that a large amount of the mass of a big star is concentrated in a point. The precise nature of what a singularity actually is usually is thought to be a question related to quantum gravity. But for regions relatively close (but not too much) to the singularity classical relativity still holds and it is expected that neighbouring matter would be attracted to the singularity. The inexistence of the event horizon means that there is the possibility of going arbitrarily near the singularity and returning to the original point (well, if tide forces don´t kill you and such that). In particular light can go near the singularity and scape to a distant observer so we can see what happens there. But even thought some matter in certain trajectories could scape I think that it is reasonable that most of the matter would be trapped in the singularity. Intuitively one would think that that increases the mass of the singularity and that it sooner or later it will become a black hole. Possibly that is a too naive way of think and that is one of the particularities of the singularity (but I am not sure about it).
Anyway, if singularities re shown to be possible (at least for a certain time) one could try to consider if they are distinguishable from black holes. The answer is in the positive. Even one could try a little bit further and consider the possibility that an existing black hole could break and leave behind the singularity. The most natural case would be kerr black hole which is led to rotate faster than it´s extremal limit. Because astrophysical black holes are usually believed to be Kerr ones one immediately can answer for particular observable signatures of this breaking. ONe arxiv article where one can read the details is this: Magnification relations for Kerr lensing and testing Cosmic Censorship. There are described some mathematical details of calculations made on the pna (post Newtonian approximation)of some optical effects. The author claim that the differences in behaviour among black holes and naked singularities could be observed with the incoming new generation of available technology.
From the viewpoint of an string theorist 4 dimensions are very restrictive, what about the influence of additional dimensions? You can read a paper about the particular: Spherical gravitational collapse in N-dimensions. It is co-authored by Joshi and the answer is mildly positive. I recommend to read the considerations that he makes in the conclusions.
A later thing I am going to discuss is the role of quantum gravity. If naked singularities actually exist they are a window to do observations of quantum gravitational effects (or at least one so expects). But before going there one could answer if quantum gravity considerations modify the classical predictions of formation of naked singularities. I don´t know the "asscendence" of Joshi, tat is, if he is an string theoretic oriented or an LQG oriented researcher. Being an specialist in general relativity one, maybe, would expect him being an LQG researcher, but reading his papers I guess that a better fir would be to consider him a "naked singularity phenomenologist". Anyway, LQG is easier to learn that string theory and is accepted by a plausible quantum gravity by hundreds of people with a tenures/investigation positions in universities so it is reasonable to expect some paper using LQG to investigate the question. And, effectively, there is such paper: Quantum evaporation of a naked singularity.
This papers point in a different direction that the classical results. Using a toy model with an scalar field (in a way similar to loop quantum cosmology calculations) it is shown that near the should be singularity gravity becomes a repulsive force and the naked singularity isn't formed. I guess that one must understand that this calculations make sense in the case where the classical equations point to the formation of the singularity. That is, classically one expect the formation of the naked singularity, but looking at quantum phenomena one sees that actually the singularity is avoided. I must clarify that this calculations are not claimed to be fully quantum by the authors and they still believe that in full quantum sceneries the naked singularity would easily reappear.
Still this last scenery could have relevant observational consequences in the form of powerful gamma ray bursts that result in the evaporation of the should be singularity. The precise signature of that bursts depend in some free factors of the theory, and, in particular, the claim that can be used to estimate a value of LQG, j, the value of the representation of (complex) SU(2) used.
Well, certainly I don´t believe that string theory people would take too seriously this considerations, but claiming possible near future experimental results I believe it well deserves to say something about the subject.
In fact actually there are some results in string theory about singularities, particularly the enhanchon mechanism, but it is related to "educated" singularities inside a black hole who are prudent enough to not show themselves naked. Abut black holes in string theory I hope to write a post soon.
To end this post to leave a link to a self claimed naked singularity who is kind enough have a blog (in Spanish), that links to this: La Singularidad Desnuda.
The author, Pankaj S. Joshi, seems to be an total expert in the subject (a common issue in Scientific American)and has a recent book- from 2008- about the particular,
Gravitational Collapse and Spacetime Singularities.
I didn´t read the book, but I found the article interesting so I searched in wikipedia and some of the papers linked there. I´ll try to explain some of the aspects now.
In general relativity there are two well known places where singularities appear, black holes and cosmology. The most naive way of thinking/defining singularities is to characterise them as points where the metric (or curvature) of space-time becomes infinite. According to that the event horizon of a Schwarschild black hole would be a singularity. It was realized that that infinity was due to a bad choice of coordinates. In that solution the centrer of the black hole, the R=0 point, also get an infinity value and this can´t be overcome by any other choice of coordinates so it is a genuine singularity.
As far as we like to have coordinate free definitions there is more technical definition, a singularity is defined to be one which contains geodesics which cannot be extended in a smooth manner. The end of such a geodesic is considered to be the singularity. That definition is useful to probe theorems (as did Penrose and Hawkings in the 70´s) about how singularities can´t be avoided in classical general relativity in cosmological sceneries. It also permit to make a diferentiation about coordinate singularities, the ones I talked before, related to black holes, and what are known as conical singularities, related to things such as cosmic strings. A conical singularity occurs when there is a point where the limit of every diffeomorphism invariant quantity is finite. In which case, spacetime is not smooth at the point of the limit itself. Thus, spacetime looks like a cone around this point, where the singularity is located at the tip of the cone. The metric can be finite everywhere if a suitable coordinate system is used.
The S.A article treats about singularities associated to gravitational collapse. There exists what is known like the cosmic censorship conjecture (or hypothesis) , own to Roger Penrose, which states that there are not naked singularities. That is, every singularity must be hidden behind an event horizon and cant be seen from the outside. It has the status of conjecture because it hasn´t be proved in a rigorous way under physically reasonable assumptions. In fact it hasn´t even stated in a mathemathical rigorous way.
The article, obviously, try to answer the conjecture in the negative. Before describing it's arguments I´ll talk about an aspect closely related to the CCC. If one examines the solutions for rotating black holes (Kerr solution) one sees that if is allowed that J, the angular momentum is greater than the mass M of the black hole, that is J/M>1 a naked singularity (a ringed shaped one) appears. A similar thing goes for charged (electric of whatever associated to U(1) gauge symmetry)black hole solutions (Reissner-Nordstom black holes) where a naked singularity appears if the charge, Q, is greater than the mass of the b-h, i.e., Q/M>1. It is commonly assumed that the CCC holds and the case where the equality would arise are called extremal black holes. The possibility of a reverse, negative, sign in the above expressions is not even contemplated in most theoretical considerations.
That´s a reason why I was somewhat surprised when I read the article and saw that in fact when one makes actual calculations, in classical general relativity, of how gravitational collapse behaves when some oversimplifying assumptions about the state of the star are neglected naked singularities actually are shown to be possible.
If the star is perfectly spherically symmetric and of uniform density everything is o.k and the black hole is formed. But relaxing one of the assumptions separately(or both at once) it can be shown that naked singularities actually appear.
Intuitively the reason is, for the case of non uniform density, that it can happen that the rate of accretion into the centre is never fast enough to actually form an even horizon and a central, unique, singularity appears. In the case of non sphericity it is shown that the collapse is neither spheric so the mass is concentrated in two points that become singularities at the end of the collapse avoiding the formation of the event horizon because of the oblong shape of the infalling matter that forbids the concentration of enough mass inside the Schwarschild radius.
Once that this facts are established one can wonder about how realistic and stable are. After all they mean that a large amount of the mass of a big star is concentrated in a point. The precise nature of what a singularity actually is usually is thought to be a question related to quantum gravity. But for regions relatively close (but not too much) to the singularity classical relativity still holds and it is expected that neighbouring matter would be attracted to the singularity. The inexistence of the event horizon means that there is the possibility of going arbitrarily near the singularity and returning to the original point (well, if tide forces don´t kill you and such that). In particular light can go near the singularity and scape to a distant observer so we can see what happens there. But even thought some matter in certain trajectories could scape I think that it is reasonable that most of the matter would be trapped in the singularity. Intuitively one would think that that increases the mass of the singularity and that it sooner or later it will become a black hole. Possibly that is a too naive way of think and that is one of the particularities of the singularity (but I am not sure about it).
Anyway, if singularities re shown to be possible (at least for a certain time) one could try to consider if they are distinguishable from black holes. The answer is in the positive. Even one could try a little bit further and consider the possibility that an existing black hole could break and leave behind the singularity. The most natural case would be kerr black hole which is led to rotate faster than it´s extremal limit. Because astrophysical black holes are usually believed to be Kerr ones one immediately can answer for particular observable signatures of this breaking. ONe arxiv article where one can read the details is this: Magnification relations for Kerr lensing and testing Cosmic Censorship. There are described some mathematical details of calculations made on the pna (post Newtonian approximation)of some optical effects. The author claim that the differences in behaviour among black holes and naked singularities could be observed with the incoming new generation of available technology.
From the viewpoint of an string theorist 4 dimensions are very restrictive, what about the influence of additional dimensions? You can read a paper about the particular: Spherical gravitational collapse in N-dimensions. It is co-authored by Joshi and the answer is mildly positive. I recommend to read the considerations that he makes in the conclusions.
A later thing I am going to discuss is the role of quantum gravity. If naked singularities actually exist they are a window to do observations of quantum gravitational effects (or at least one so expects). But before going there one could answer if quantum gravity considerations modify the classical predictions of formation of naked singularities. I don´t know the "asscendence" of Joshi, tat is, if he is an string theoretic oriented or an LQG oriented researcher. Being an specialist in general relativity one, maybe, would expect him being an LQG researcher, but reading his papers I guess that a better fir would be to consider him a "naked singularity phenomenologist". Anyway, LQG is easier to learn that string theory and is accepted by a plausible quantum gravity by hundreds of people with a tenures/investigation positions in universities so it is reasonable to expect some paper using LQG to investigate the question. And, effectively, there is such paper: Quantum evaporation of a naked singularity.
This papers point in a different direction that the classical results. Using a toy model with an scalar field (in a way similar to loop quantum cosmology calculations) it is shown that near the should be singularity gravity becomes a repulsive force and the naked singularity isn't formed. I guess that one must understand that this calculations make sense in the case where the classical equations point to the formation of the singularity. That is, classically one expect the formation of the naked singularity, but looking at quantum phenomena one sees that actually the singularity is avoided. I must clarify that this calculations are not claimed to be fully quantum by the authors and they still believe that in full quantum sceneries the naked singularity would easily reappear.
Still this last scenery could have relevant observational consequences in the form of powerful gamma ray bursts that result in the evaporation of the should be singularity. The precise signature of that bursts depend in some free factors of the theory, and, in particular, the claim that can be used to estimate a value of LQG, j, the value of the representation of (complex) SU(2) used.
Well, certainly I don´t believe that string theory people would take too seriously this considerations, but claiming possible near future experimental results I believe it well deserves to say something about the subject.
In fact actually there are some results in string theory about singularities, particularly the enhanchon mechanism, but it is related to "educated" singularities inside a black hole who are prudent enough to not show themselves naked. Abut black holes in string theory I hope to write a post soon.
To end this post to leave a link to a self claimed naked singularity who is kind enough have a blog (in Spanish), that links to this: La Singularidad Desnuda.
Sunday, May 18, 2008
Black holes information distortion paradox
A few days ago a friend of mine, graduate theoretical physician, but not an active physician nowadays, and an ocasional reader of this blog,let me know of a new in the media versing about a resolution of the "black hole information paradox". The new was published in many webs, for example here. By the same time a thread was opened in physics phorums about the topic, concretelly Physicists Demonstrate How Information Can Escape From Black Holes based in LQG.
Ok, I suposse that I would have to somehow give an opinion about the new. I have waited a bit to see if, apart of physics phorums people, some of the big (or even not so bigs) ones on the blogosphere said something about the particular. Afther all Astekhar, the mainauthor of the paper behind the new, is one of the greatests personalities in LQG (the whole field begins with a work of him about new variables in canonical gravity) and the theme is very catchy, to say the less. For some reason there has not been such an entry in referential blogs, so I´ll try to give my humble opinion abot the particular.
First of all to say that I find that the claim of the new somewhat distort the actual nature of the achivement. Suposedly the paper solves the questions in the framework of LQG. Afther all in the news release you can read:
"Once we realized that the notion of space-time as a continuum is only an approximation of reality, it became clear to us that singularities are merely artifacts of our insistence that space-time should be described as a continuum."
The idea of discrete space-time strongly suggest that they are talking about LQG. Well, in the physics porum post somone pointed to the arxiv paper behind the news release, concretelly this, Information is Not Lost in the Evaporation of 2-dimensional Black Holes. The first bad thing comes in the title, "2-dimensional black holes". That is they solve the problem in a simplified modell, that always opens the possibilitie that the problem could not be solved in the full environment, afther all 3-d quantum gravity is very diferent from 4-d one.
Anyway, let´s see what is going on. In the last post I talked about LQG and I did a brief description of how LQG treats black holes (or at least one of the ways they do it when they face the singularity problem). As not every reader of this blog is assumed to speak spanish I´ll re-explain it. They don´t work in the full LQG framework but in modell with reduced simmetry. They get the Scharschild solution (a solution for vacuum Einstei equations, statif and with radial symmetry) and write the hamiltonial constraint equation fo it. They treat the radious as a discrete time coordinate. That results in a diference equation that can be solved and they show that they can evolve the solution for negative values of the radious, so they, seemengly, advoid the central singularity. Before reading the paper of Astekharet all I tried to figure how they could have procceded. To begin with the information paradox problem is related to matter in the vecinity of the horizont. So they would need to introduce in the description mttr in some wayor another. The original work of Hawkings that raised the whole problem used a fiexed Schwarschild background and an scalar field propagating in it. By the properties of quantization of fields in a courved backgrounds it was known that a vacuum state contianing no particles for aan observer is transformed in a state containg particles by a bogoliougov transformation for another non inertial observer. Playing with that, and with the conformal diagrams of black holes, Hawking derived that black holes actually emit radiation, in thermal quilibrium. That raises the problem that the black hole aan evaaporate because that procces. But the b-h was formed by matter in a pure state, and the thermally described matter is in a mixed stte, so the evolution would be not unitary (that is a bried description of the problem we are trating, for the ssafe of someone wouldn´t know it). Canonical LQG, the one in which Astekhar usually works, normally trates pure gravity, althought it can describe non fermionic matter also. Knowing that I thoguht that they would use some variant of the singularity removal approach including a klein-gordon field. Well, I was too naive.
They work in something called "Callen-Giddings-Harvey-Strominger (CGHS) black holes". I had not previous knowledge of that model, but the names behind it sound me "stringy", in particular Strominger is mainly an string theorist. Well, I was not wrong this time. The paper makes begins with a brief description of the hawking problems, some previous aproachs to the solution (açone by Hawking himself aaproach based in the maldacnena AdS/CFT corresondence) and just afther that talks about some workd in the early ninties triying to solve it in a toy two dimensional modell, the CGHS.
Just before writing the actual equation of the model the aouthor make a very courious advise:
"Although our
considerations are motivated by loop quantum gravity, in
this Letter we will use the more familiar Fock quantization
since the main argument is rather general"
So they say that we are not going to see a formalism related to LQG, alathought LQG is behing the scene. Well, that means taht we must belief in LQG, but we are not ging to see it. Ok, lets belive, at least for a while. Let´s see (part of)the lagrangian describing the model:
...
Now it is when one can beguin to be really surprised. We have that Phi is said to be a dilaton. But a dilaton is a field related to string theory. All of the strings theories have a dilaton. So we are in a modell inspired by string theory (an aspect that it is not mentionesd anywhere in the paper). R is the curvature and f is an scalar field. Well, ok, no problem, someone would expect their appearence.
Afther that they introduce the equatios associated to the lagrangian and begins the task of finding solutons resembling a black hole suited for their purposes. First they affront the classical case. They do it in a perturbative, recoursive, way. That is, they choose a candidate metric, calculate the stress tensor for the fields and reintroduce it in the Einstein equation. By dong that they find that the metric an develope a singularity that they can identify as a proper black hole.
Afther that they consider a quantized version, they add hats xD). Not, serously, they use a fock space tratement (in teh spirit of the Wald aproach to quantization in courved backgrounds, but this time quantizing the metric also). They afrront the uestion of quantization (solving the conmutator eqations to say that) by a bootstrapping procedure, a recoursive way similar to the classical one. They do the suual stuff of identifiying the average values with the classical solutions,but they face a problem when the metric becomes singular, and they cann not continuate the bootstraping. Afther that they use another procedure, a mean field approach MFA. They argue that the e relevant part to solve the information paradox depends on the behaviour of the MFA in the near future ifinity and with some 3 extra sumptions ( they explain that two of them aare commonly accepted and that the other is very natural) they can calculate the S-Matrix and se that it is unitary.
Well, the detaills of how valids are the asumptions (2-D space time, MFA, asymtotic regions, etc) is something that, fourtunately, I don´t need to judge. The key point that I want to raise is that what we see in the paper is very, very, far from any formalisms related to LQG. So to claim that this can be seem as a trioumph of LQG, if they don´t bring a future a paper (or smewhat point me that I am missing something important) where they addapt the calculations to something more LQG like, is to somewhat distort the truth. Or, at least, a too propagandistic deformation of facts ;-).
P.S. Seriously, I would like to leave this tasks to the famous physicists bloggers. For example, I am still wating Sean Carrol to post about the 't Hoof paper I writted about two posts above.
Ok, I suposse that I would have to somehow give an opinion about the new. I have waited a bit to see if, apart of physics phorums people, some of the big (or even not so bigs) ones on the blogosphere said something about the particular. Afther all Astekhar, the mainauthor of the paper behind the new, is one of the greatests personalities in LQG (the whole field begins with a work of him about new variables in canonical gravity) and the theme is very catchy, to say the less. For some reason there has not been such an entry in referential blogs, so I´ll try to give my humble opinion abot the particular.
First of all to say that I find that the claim of the new somewhat distort the actual nature of the achivement. Suposedly the paper solves the questions in the framework of LQG. Afther all in the news release you can read:
"Once we realized that the notion of space-time as a continuum is only an approximation of reality, it became clear to us that singularities are merely artifacts of our insistence that space-time should be described as a continuum."
The idea of discrete space-time strongly suggest that they are talking about LQG. Well, in the physics porum post somone pointed to the arxiv paper behind the news release, concretelly this, Information is Not Lost in the Evaporation of 2-dimensional Black Holes. The first bad thing comes in the title, "2-dimensional black holes". That is they solve the problem in a simplified modell, that always opens the possibilitie that the problem could not be solved in the full environment, afther all 3-d quantum gravity is very diferent from 4-d one.
Anyway, let´s see what is going on. In the last post I talked about LQG and I did a brief description of how LQG treats black holes (or at least one of the ways they do it when they face the singularity problem). As not every reader of this blog is assumed to speak spanish I´ll re-explain it. They don´t work in the full LQG framework but in modell with reduced simmetry. They get the Scharschild solution (a solution for vacuum Einstei equations, statif and with radial symmetry) and write the hamiltonial constraint equation fo it. They treat the radious as a discrete time coordinate. That results in a diference equation that can be solved and they show that they can evolve the solution for negative values of the radious, so they, seemengly, advoid the central singularity. Before reading the paper of Astekharet all I tried to figure how they could have procceded. To begin with the information paradox problem is related to matter in the vecinity of the horizont. So they would need to introduce in the description mttr in some wayor another. The original work of Hawkings that raised the whole problem used a fiexed Schwarschild background and an scalar field propagating in it. By the properties of quantization of fields in a courved backgrounds it was known that a vacuum state contianing no particles for aan observer is transformed in a state containg particles by a bogoliougov transformation for another non inertial observer. Playing with that, and with the conformal diagrams of black holes, Hawking derived that black holes actually emit radiation, in thermal quilibrium. That raises the problem that the black hole aan evaaporate because that procces. But the b-h was formed by matter in a pure state, and the thermally described matter is in a mixed stte, so the evolution would be not unitary (that is a bried description of the problem we are trating, for the ssafe of someone wouldn´t know it). Canonical LQG, the one in which Astekhar usually works, normally trates pure gravity, althought it can describe non fermionic matter also. Knowing that I thoguht that they would use some variant of the singularity removal approach including a klein-gordon field. Well, I was too naive.
They work in something called "Callen-Giddings-Harvey-Strominger (CGHS) black holes". I had not previous knowledge of that model, but the names behind it sound me "stringy", in particular Strominger is mainly an string theorist. Well, I was not wrong this time. The paper makes begins with a brief description of the hawking problems, some previous aproachs to the solution (açone by Hawking himself aaproach based in the maldacnena AdS/CFT corresondence) and just afther that talks about some workd in the early ninties triying to solve it in a toy two dimensional modell, the CGHS.
Just before writing the actual equation of the model the aouthor make a very courious advise:
"Although our
considerations are motivated by loop quantum gravity, in
this Letter we will use the more familiar Fock quantization
since the main argument is rather general"
So they say that we are not going to see a formalism related to LQG, alathought LQG is behing the scene. Well, that means taht we must belief in LQG, but we are not ging to see it. Ok, lets belive, at least for a while. Let´s see (part of)the lagrangian describing the model:
...Now it is when one can beguin to be really surprised. We have that Phi is said to be a dilaton. But a dilaton is a field related to string theory. All of the strings theories have a dilaton. So we are in a modell inspired by string theory (an aspect that it is not mentionesd anywhere in the paper). R is the curvature and f is an scalar field. Well, ok, no problem, someone would expect their appearence.
Afther that they introduce the equatios associated to the lagrangian and begins the task of finding solutons resembling a black hole suited for their purposes. First they affront the classical case. They do it in a perturbative, recoursive, way. That is, they choose a candidate metric, calculate the stress tensor for the fields and reintroduce it in the Einstein equation. By dong that they find that the metric an develope a singularity that they can identify as a proper black hole.
Afther that they consider a quantized version, they add hats xD). Not, serously, they use a fock space tratement (in teh spirit of the Wald aproach to quantization in courved backgrounds, but this time quantizing the metric also). They afrront the uestion of quantization (solving the conmutator eqations to say that) by a bootstrapping procedure, a recoursive way similar to the classical one. They do the suual stuff of identifiying the average values with the classical solutions,but they face a problem when the metric becomes singular, and they cann not continuate the bootstraping. Afther that they use another procedure, a mean field approach MFA. They argue that the e relevant part to solve the information paradox depends on the behaviour of the MFA in the near future ifinity and with some 3 extra sumptions ( they explain that two of them aare commonly accepted and that the other is very natural) they can calculate the S-Matrix and se that it is unitary.
Well, the detaills of how valids are the asumptions (2-D space time, MFA, asymtotic regions, etc) is something that, fourtunately, I don´t need to judge. The key point that I want to raise is that what we see in the paper is very, very, far from any formalisms related to LQG. So to claim that this can be seem as a trioumph of LQG, if they don´t bring a future a paper (or smewhat point me that I am missing something important) where they addapt the calculations to something more LQG like, is to somewhat distort the truth. Or, at least, a too propagandistic deformation of facts ;-).
P.S. Seriously, I would like to leave this tasks to the famous physicists bloggers. For example, I am still wating Sean Carrol to post about the 't Hoof paper I writted about two posts above.
Subscribe to:
Posts (Atom)
