Collapsing shells of radiation in anti-de Sitter spacetimes and the hoop and cosmic censorship conjectures

Gravitational collapse of radiation in an anti-de Sitter background is studied. For the spherical case, the collapse proceeds in much the same way as in the Minkowski background, i.e., massless naked singularities may form for a highly inhomogeneous collapse, violating the cosmic censorship, but not the hoop conjecture. The toroidal, cylindrical and planar collapses can be treated together. In these cases no naked singularity ever forms, in accordance with the cosmic censorship. However, since the collapse proceeds to form toroidal, cylindrical or planar black holes, the hoop conjecture in an anti-de Sitter spacetime is violated.Comment: 4 pages, Revtex Journal: to appear in Physical Review

Exact General Relativistic Perfect Fluid Disks with Halos

Using the well-known ``displace, cut and reflect'' method used to generate disks from given solutions of Einstein field equations, we construct static disks made of perfect fluid based on vacuum Schwarzschild's solution in isotropic coordinates. The same method is applied to different exactsolutions to the Einstein'sequations that represent static spheres of perfect fluids. We construct several models of disks with axially symmetric perfect fluid halos. All disks have some common features: surface energy density and pressures decrease monotonically and rapidly with radius. As the ``cut'' parameter $a$ decreases, the disks become more relativistic, with surface energy density and pressure more concentrated near the center. Also regions of unstable circular orbits are more likely to appear for high relativistic disks. Parameters can be chosen so that the sound velocity in the fluid and the tangential velocity of test particles in circular motion are less then the velocity of light. This tangential velocity first increases with radius and reaches a maximum.Comment: 22 pages, 25 eps.figs, RevTex. Phys. Rev. D to appea

Gravitational Collapse of Perfect Fluid in Self-Similar Higher Dimensional Space-Times

We investigate the occurrence and nature of naked singularities in the gravitational collapse of an adiabatic perfect fluid in self-similar higher dimensional space-times. It is shown that strong curvature naked singularities could occur if the weak energy condition holds. Its implication for cosmic censorship conjecture is discussed. Known results of analogous studies in four dimensions can be recovered.Comment: 11 Pages, Latex, no figures, Accepted in Int. J. Mod. Phys.

Two-Dimensional Black Holes and Planar General Relativity

The Einstein-Hilbert action with a cosmological term is used to derive a new action in 1+1 spacetime dimensions. It is shown that the two-dimensional theory is equivalent to planar symmetry in General Relativity. The two-dimensional theory admits black holes and free dilatons, and has a structure similar to two-dimensional string theories. Since by construction these solutions also solve Einstein's equations, such a theory can bring two-dimensional results into the four-dimensional real world. In particular the two-dimensional black hole is also a black hole in General Relativity.Comment: 11 pages, plainte

Does a relativistic metric generalization of Newtonian gravity exist in 2+1 dimensions?

It is shown that, contrary to previous claims, a scalar tensor theory of Brans-Dicke type provides a relativistic generalization of Newtonian gravity in 2+1 dimensions. The theory is metric and test particles follow the space-time geodesics. The static isotropic solution is studied in vacuum and in regions filled with an incompressible perfect fluid. It is shown that the solutions can be consistently matched at the matter vacuum interface, and that the Newtonian behavior is recovered in the weak field regime.Comment: 6 pages, no figures, Revtex4. Some discussions on the physical nature of the interior solution and on the omega->infinity limit and some references added. Version to appear in Phys. Rev.

Quasi-normal modes of toroidal, cylindrical and planar black holes in anti-de Sitter spacetimes: scalar, electromagnetic and gravitational perturbations

We study the quasi-normal modes (QNM) of scalar, electromagnetic and gravitational perturbations of black holes in general relativity whose horizons have toroidal, cylindrical or planar topology in an asymptotically anti-de Sitter (AdS) spacetime. The associated quasinormal frequencies describe the decay in time of the corresponding test field in the vicinities of the black hole. In terms of the AdS/CFT conjecture, the inverse of the frequency is a measure of the dynamical timescale of approach to thermal equilibrium of the corresponding conformal field theory.Comment: Latex, 16 pages. Minor change

The Three-Dimensional BTZ Black Hole as a Cylindrical System in Four-Dimensional General Relativity

It is shown how to transform the three dimensional BTZ black hole into a four dimensional cylindrical black hole (i.e., black string) in general relativity. This process is identical to the transformation of a point particle in three dimensions into a straight cosmic string in four dimensions.Comment: Latex, 9 page

Gravitational collapse to toroidal, cylindrical and planar black holes

Gravitational collapse of non-spherical symmetric matter leads inevitably to non-static external spacetimes. It is shown here that gravitational collapse of matter with toroidal topology in a toroidal anti-de Sitter background proceeds to form a toroidal black hole. According to the analytical model presented, the collapsing matter absorbs energy in the form of radiation (be it scalar, neutrinos, electromagnetic, or gravitational) from the exterior spacetime. Upon decompactification of one or two coordinates of the torus one gets collapsing solutions of cylindrical or planar matter onto black strings or black membranes, respectively. The results have implications on the hoop conjecture.Comment: 6 pages, Revtex, modifications in the title and in the interpretation of some results, to appear in Physical Review