## Sunday, May 25, 2008

### Wormholes at the LCH?

The LCH is next to open. Hopefully supersymmetry and the Higgs boson will be found. But there are more possible things that we can find there. The recent Planck 2008 congress was devoted to that topic. You can see blog entries covering that in the Dmitry (non equilibrium phenomena) blog, concretely this entry, and previous ones (ok, the entry with the interview to Polyakov is not about Planck 2008, but it is worth reading anyway). Another ongress, PPC2008 was devoted to LHC, and string phenomenology in general. You can read blog entries about it in Tomasso Dorigos blog, particularly in this entry and subsequent ones (advise, there are a lot of them). Another coverage of the congress is here. If some reader has a lot of time and is interested in reading still more about scientific congress and phenomenology he could read the coverage that Marni Dee has made of neutrinos 2008. At the monet of writing this entry her las post is this.

Well, i am going to add some fuel into the phenomenology of LCH possible predictions in this post. I am going to talk about wormholes production in LCH. That possibility heavily relies in the large extra dimensions scenario. You can read a post in the thomaso dorigos series on PPC2008 about the subject, this. Also you could read my own post about large extra dimensions and warped geometries.

As I said in that entry one thing that can possibly found in the LHC, if the LED sceneries are true, are microblack holes. But that is not the whole history. One can find another things such as p-branes or wormholes. You can read about the formers in this paper. Advise, there they talk about a somewhat peculiar type of p-branes, cosmic branes, introduced in this other paper. I am not going to describe those papers, just quote the abstract, which is self explanatory:

We compute the cross section for p-brane creation by super-Planckian scattering processes
in a (n +4)-dimensional space-time with n−m flat large extra dimensions and m
flat small dimensions of size of the fundamental gravitational scale. We find that the
cross section for the formation of a brane with dimension 1 ≤ p ≤ m, completely wrapped
on the small dimensions, is larger than the cross section for the creation of a spherically
symmetric black hole. Therefore, in space times with asymmetric compactifications we
predict that branes are more likely to be created in super-Planckian scattering processes
than black holes. The higher rate of p-brane production significantly enhances possible
detection of non-perturbative gravitational events by future hadron colliders and cosmic
rays detectors.

Now I am going, at last, with the actual topic of this post. I will explain the resuoults of two papers, Time Machine at the LHC and If LHC is a Mini-Time-Machines Factory, Can We Notice?.

The first paper face the question of the actal calculation of the probability of the wormhole beeing formed. The second, the sing that it could leave in the LHC if it actually forms.

The first paper begins with a brief review of how calculation of black hole formation can be obtained. That subject is generically know under the name of "planckian scattering". He beguines with a "quantum gravity" approach, based on the wheeler-de Witt formalism. There the possibility of black hole formation is calculated by considering the kernell of the following transtion amplitude:

$\langle h'', \phi'',\Sigma''|h', \phi',\Sigma'i\rangle= \int exp{i/\hbar S[g,\Psi]}DgDh$

The key in that approach is to study the transition between geometries describing two particles and the geometry describing black holes (or wormholes). For the details the authors refers to the paper of arxiv gr-qc/9404036. which, unfortunately, is unavailable seemingly due to a corruption in the latex that arxiv uses to render the pdf.

Other approach discussed in that brief review of black hole formation is to suppose that that ultra-relativistic particles are represented by plane gravitational waves, which interacting collide and produce a black hole. For 3D geometry the energies required are not available in the LHC, but in the LED sceneries the thing changes. The Schwarzschild radius of a 4+n dimensional black hole of mass M = √s is approximately:

$r_o \approx M^{-1}_{4+n} (s/M^{2}_{4+n})^{1/2n +1)$

( is the square of the center of mass energy of colliding particles, M4+n is the 4+n dimensional Planck mass and the 4 dimensional Planck mass is given by:

$M^2_{pl} \approx V_n M^{2 + n}_{4+n}$

Where Vn is the volume of the extra dimensions. This problem can be achieved using the Aichelburg-Sexl metric, which describe a particle at ultra relativistic speeds and is obtained by doing a Lorentz boost to the Schwarzschild metric and some convenient changes of variables. In the article the details of the calculations are not presented and the author refers to the literature. Maybe some reader is surprised why string theory is not mentioned in this article to analyze the formation of black holes. I guess that it is a good idea to give some things about it. Of course the ultimate reason to even bother about practical formation of black holes depends on warped dimensions. Although warped dimensions can be studied by classical general relativity in 4+1 dimensions (for one warped dimension) the practical motivation to do that depends on string theory. Ok, that was clear, I guess, so I´ll say some quick ideas about string theory and black holes. String theory can describe black holes of an special type, Reissner-Nordstrom black holes, using Dp-branes, and calculate it´s entropy. But the approach used to describe that black holes doesn´t say nothing about the actual formation of them. AS soon as in the eighties that question was studied by Veneziano who calculated the possibility of black hole formation by exchange of gravitons in a sting theoretic description. I don´t really know why exactly that approaches are not followed, but at least I leave Constance of their existence.

The article follows with a very brief introduction to wormholes. That is a topic widely discussed in the net. The reader can find references to it in many places. To avoid to make this entry too long I have made a separate entry in my other blog. I must apologize for English readers because the entry is written in Spanish, anyway, the actual url for it is this.

Anyway, in that entry I only discuss the basic of wormholes. For the article discussed here it is necessary to consider wormholes in a braneworld scenario. There, where the Universe is considered as a 3-brane embedded in a D-dimensional bulk, the four-dimensional Einstein field equations contain the effective four-dimensional stress energy tensor:

$G_{\nu\mu}= M^{-1}_{pl}.T^{eff}_{\nu\mu}$

The effective energy momentum tensor is a sum of the stress energy tensor of a matter confined on the brane, Tμv and correction terms that arise from a projection of the D-dimensional Einstein equation to the four-dimensional space-time. For some particular examples it is possible to show that the four-dimensional effective stress energy tensor violates the NEC meanwhile the total five-dimensional stress energy tensor does respect the NEC.

After discussing how wormholes are described in branworld sceneries the actual question of their formation is discussed. The approach followed mimetizes the approach followed for black holes. It is not very detailed and it is based in the following cross section:

$\sigma pp\rightarrow wh(s) \approx \sum_{i,j}\int_{\tau_m}^1 d\tau \int_{\tau}^1 dx/x fi(x)fj(\tau/x)\sigma ij\rightarrow wh(\tau s)$

Here √s is the center of mass energy, x and τ/x are the parton momentum fractions, and fi are the parton distribution functions. The parameter τm = M2min/s where Mmin corresponds to the minimum mass for a valid wormhole description.

σij→wh(s) is the geometrical cross section of the wormhole production and depends in a form factor F. The form factor F(√s/MD) incorporates the theoretical uncertainties in description of the process, such as the amount of the initial center mass energy that goes into the wormhole, the distribution of wormhole masses as function of energy. These corrections are similar to corrections in the formula for black hole production.

The second paper centers on the description of the observable traces of the existence of a wormhole. Much emphasizes is made in the possibility of the wormhole behaving as a time machine. For this it´s two motous must be shifting away at a considerable speed for some lapse of time. Anyway, the authors prefer to use MTM (minitime machine) instead of wormhole. Anyway the actual possibilities of detection discussed in the paper can be summarized as follows:

(i) change of the energy spectrum due to the frequency-filtration property of MTM,
(ii) possible production of anomalously energetic particles, accelerated by passing many times
through gravitational field inside the MTM,
(iii) acceleration of particle decays, since the proper time of a particle moving inside MTM can
strongly exceed the laboratory time,
(iv) CPT and naive unitarity violation (thermalization) due to effective non-local interactions
caused by MTM and to possible ambiguity in the population of closed world-lines inside MTM,
(v) collective effects due to conversion of a single particle into a bunch of its co-existing copies
within the MTM