Wednesday, June 07, 2006

Gr-qc papers for Wednesday

John Barrow, Douglas Shaw, and Christos Tsagas study general cosmological solutions of 2+1-dimensional general relativity. In four dimensions, general enough solutions often happen to be non-integrable or even chaotic. Whenever you're drunk and you can only measure the spacetime dimension plus minus one or so, you have a chance to simplify the general relativistic description of your Universe.

The reason is that in three spacetime dimensions, life of general relativists is easier (although the life of mammals is harder). The Riemann tensor R_{abcd} contains the same six components as the Ricci tensor R_{ab}. Consequently, the Weyl tensor vanishes identically and the Riemann tensor can be written purely in terms of the Ricci tensor. That means that there are no bulk excitations of gravity and the gravitational field is determined entirely in terms of the matter that sources the field. The authors consider static dust and moving dust and they find the exact solutions in many cases. They also study the stability of those cosmologies and determine that they are indeed stable, at least neutrally.

Gerard 't Hooft offers a very interesting proposal about some unusual dynamics that might occur at black hole horizons. The horizon is a null-spatial-spatial hypersurface which makes it possible to treat it as a limiting case of a space-like hypersurface. The electromagnetic fields and other fields are treated as an additional algebra. They provide you with quantum hair that carries the entropy and remembers the past. For some reasons (that have already appeared in the literature but I don't understand them), 't Hooft considers a Higgs field that breaks the electromagnetic U(1) - a superconductor at the horizon is something that may attract George Chapline.

The calculations involve a lot of logarithms and delta-functions of "sigma", the transverse coordinates to the horizon. 't Hooft speculates that the representations of his algebra associated with the horizon will have a finite dimension and will yield the right black hole entropy. This computation could be relevant for non-supersymmetric (or general) black holes in string theory, he proposes. The newest point in this paper is an attempt to include non-Abelian gauge fields and solitons at the horizon within a similar framework that has only been used in the Einstein-Maxwell case previously.

Christian Fronsdal offers a new, unusual framework to merge general relativity with hydrodynamics that should be relevant for stars and various other cellestial bodies. Normally we assume that the stress-energy tensor has the form
  • T_{mn} = (rho + p) U_m U_n - p g_{mn}

where "U_m" is a velocity, "rho" is energy density" and "p" is pressure. The author does not like this formula due to Tolman because it requires to choose an equation of state - a relation between "p" and "rho". Fronsdal believes that it is reasonable and useful to imagine that "U_m" is a gradient of some additional scalar field - a potential for velocity - and because I don't quite believe that it is an entirely reasonable assumption, everyone who is interested should read the original paper.

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