Thermodynamics of toroidal black holes

The thermodynamical properties of toroidal black holes in the grand canonical ensemble are investigated using York's formalism. The black hole is enclosed in a cavity with finite radius where the temperature and electrostatic potential are fixed. The boundary conditions allow one to compute the relevant thermodynamical quantities, e.g. thermal energy, entropy and specific heat. This black hole is thermodynamically stable and dominates the grand partition function. This means that there is no phase transition, as the one encountered for spherical black holes.Comment: 11 pages, 2 eps figures, revte

Stationary Black Holes in a Generalized Three-Dimensional Theory of Gravity

We consider a generalized three-dimensional theory of gravity which is specified by two fields, the graviton and the dilaton, and one parameter. This theory contains, as particular cases, three-dimensional General Relativity and three-dimensional String Theory. Stationary black hole solutions are generated from the static ones using a simple coordinate transformation. The stationary black holes solutions thus obtained are locally equivalent to the corresponding static ones, but globally distinct. The mass and angular momentum of the stationary black hole solutions are computed using an extension of the Regge and Teitelboim formalism. The causal structure of the black holes is described.Comment: 12 pages, Late

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

The Two-Dimensional Analogue of General Relativity

General Relativity in three or more dimensions can be obtained by taking the limit $\omega\rightarrow\infty$ in the Brans-Dicke theory. In two dimensions General Relativity is an unacceptable theory. We show that the two-dimensional closest analogue of General Relativity is a theory that also arises in the limit $\omega\rightarrow\infty$ of the two-dimensional Brans-Dicke theory.Comment: 8 pages, LaTeX, preprint DF/IST-17.9

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

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

False vacuum decay: effective one-loop action for pair creation of domain walls

An effective one-loop action built from the soliton field itself for the two-dimensional (2D) problem of soliton pair creation is proposed. The action consists of the usual mass term and a kinetic term in which the simple derivative of the soliton field is replaced by a covariant derivative. In this effective action the soliton charge is treated no longer as a topological charge but as a Noether charge. Using this effective one-loop action, the soliton-antisoliton pair production rate is calculated and one recovers Stone's exponential factor and the prefactor of Kiselev, Selivanov and Voloshin. The results are also valid straightforwardly to the problem of pair creation rate of domain walls in dimensions greater than 2.Comment: 12 pages, Late

BLACK HOLES IN THREE-DIMENSIONAL DILATON GRAVITY THEORIES

Three dimensional black holes in a generalized dilaton gravity action theory are analysed. The theory is specified by two fields, the dilaton and the graviton, and two parameters, the cosmological constant and the Brans-Dicke parameter. It contains seven different cases, of which one distinguishes as special cases, string theory, general relativity and a theory equivalent to four dimensional general relativity with one Killing vector. We study the causal structure and geodesic motion of null and timelike particles in the black hole geometries and find the ADM masses of the different solutions.Comment: 19 pages, latex, 4 figures as uuencoded postscript file

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