5,685 research outputs found

### 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

### Conformal entropy from horizon states: Solodukhin's method for spherical, toroidal, and hyperbolic black holes in D-dimensional anti-de Sitter spacetimes

A calculation of the entropy of static, electrically charged, black holes
with spherical, toroidal, and hyperbolic compact and oriented horizons, in D
spacetime dimensions, is performed. These black holes live in an anti-de Sitter
spacetime, i.e., a spacetime with negative cosmological constant. To find the
entropy, the approach developed by Solodukhin is followed. The method consists
in a redefinition of the variables in the metric, by considering the radial
coordinate as a scalar field. Then one performs a 2+(D-2) dimensional
reduction, where the (D-2) dimensions are in the angular coordinates, obtaining
a 2-dimensional effective scalar field theory. This theory is a conformal
theory in an infinitesimally small vicinity of the horizon. The corresponding
conformal symmetry will then have conserved charges, associated with its
infinitesimal conformal generators, which will generate a classical Poisson
algebra of the Virasoro type. Shifting the charges and replacing Poisson
brackets by commutators, one recovers the usual form of the Virasoro algebra,
obtaining thus the level zero conserved charge eigenvalue L_0, and a nonzero
central charge c. The entropy is then obtained via the Cardy formula.Comment: 21 page

### Rotating Relativistic Thin Disks

Two families of models of rotating relativistic disks based on Taub-NUT and
Kerr metrics are constructed using the well-known "displace, cut and reflect"
method. We find that for disks built from a generic stationary axially
symmetric metric the "sound velocity", $(pressure/density)^{1/2}$, is equal to
the geometric mean of the prograde and retrograde geodesic circular velocities
of test particles moving on the disk. We also found that for generic disks we
can have zones with heat flow. For the two families of models studied the
boundaries that separate the zones with and without heat flow are not stable
against radial perturbations (ring formation).Comment: 18 eps figures, to be published PR

### 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

### 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

### Local conditions for the generalized covariant entropy bound

A set of sufficient conditions for the generalized covariant entropy bound
given by Strominger and Thompson is as follows: Suppose that the entropy of
matter can be described by an entropy current $s^a$. Let $k^a$ be any null
vector along $L$ and $s\equiv -k^a s_a$. Then the generalized bound can be
derived from the following conditions: (i) $s'\leq 2\pi T_{ab}k^ak^b$, where
s'=k^a\grad_a s and $T_{ab}$ is the stress energy tensor; (ii) on the initial
2-surface $B$, $s(0)\leq -{1/4}\theta(0)$, where $\theta$ is the expansion of
$k^a$. We prove that condition (ii) alone can be used to divide a spacetime
into two regions: The generalized entropy bound holds for all light sheets
residing in the region where $s<-{1/4}\theta$ and fails for those in the region
where $s>-{1/4}\theta$. We check the validity of these conditions in FRW flat
universe and a scalar field spacetime. Some apparent violations of the entropy
bounds in the two spacetimes are discussed. These holographic bounds are
important in the formulation of the holographic principle.Comment: 10 pages, 7 figure

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