924 research outputs found
Uniqueness of the asymptotic AdS3 geometry
We explicitly show that in (2+1) dimensions the general solution of the
Einstein equations with negative cosmological constant on a neigbourhood of
timelike spatial infinity can be obtained from BTZ metrics by coordinate
transformations corresponding geometrically to deformations of their spatial
infinity surface. Thus, whatever the topology and geometry of the bulk, the
metric on the timelike extremities is BTZ.Comment: LaTeX, 8 pages, no figures, version that will appear in Class. Quant.
Gra
Curvature tensors on distorted Killing horizons and their algebraic classification
We consider generic static spacetimes with Killing horizons and study
properties of curvature tensors in the horizon limit. It is determined that the
Weyl, Ricci, Riemann and Einstein tensors are algebraically special and
mutually aligned on the horizon. It is also pointed out that results obtained
in the tetrad adjusted to a static observer in general differ from those
obtained in a free-falling frame. This is connected to the fact that a static
observer becomes null on the horizon.
It is also shown that finiteness of the Kretschmann scalar on the horizon is
compatible with the divergence of the Weyl component or
in the freely falling frame. Furthermore finiteness of is compatible
with divergence of curvature invariants constructed from second derivatives of
the Riemann tensor.
We call the objects with finite Krestschmann scalar but infinite
``truly naked black holes''. In the (ultra)extremal versions of these objects
the structure of the Einstein tensor on the horizon changes due to extra terms
as compared to the usual horizons, the null energy condition being violated at
some portions of the horizon surface. The demand to rule out such divergencies
leads to the constancy of the factor that governs the leading term in the
asymptotics of the lapse function and in this sense represents a formal analog
of the zeroth law of mechanics of non-extremal black holes. In doing so, all
extra terms in the Einstein tensor automatically vanish.Comment: 21 pages, To appear in Class. Quant. Gra
Time-Symmetric Initial Data for Multi-Body Solutions in Three Dimensions
Time-symmetric initial data for two-body solutions in three dimensional
anti-deSitter gravity are found. The spatial geometry has constant negative
curvature and is constructed as a quotient of two-dimensional hyperbolic space.
Apparent horizons correspond to closed geodesics. In an open universe, it is
shown that two black holes cannot exist separately, but are necessarily
enclosed by a third horizon. In a closed universe, two separate black holes can
exist provided there is an additional image mass.Comment: 12 pages, harvmac macro, minor changes in wordin
Entropy of Constant Curvature Black Holes in General Relativity
We consider the thermodynamic properties of the constant curvature black hole
solution recently found by Banados. We show that it is possible to compute the
entropy and the quasilocal thermodynamics of the spacetime using the
Einstein-Hilbert action of General Relativity. The constant curvature black
hole has some unusual properties which have not been seen in other black hole
spacetimes. The entropy of the black hole is not associated with the event
horizon; rather it is associated with the region between the event horizon and
the observer. Further, surfaces of constant internal energy are not isotherms
so the first law of thermodynamics exists only in an integral form. These
properties arise from the unusual topology of the Euclidean black hole
instanton.Comment: 4 pages LaTeX2e (RevTeX), 2 PostScript figures. Small corrections in
the text and the reference
When Black Holes Meet Kaluza-Klein Bubbles
We explore the physical consequences of a recently discovered class of exact
solutions to five dimensional Kaluza-Klein theory. We find a number of
surprising features including: (1) In the presence of a Kaluza-Klein bubble,
there are arbitrarily large black holes with topology S^3. (2) In the presence
of a black hole or a black string, there are expanding bubbles (with de Sitter
geometry) which never reach null infinity. (3) A bubble can hold two black
holes of arbitrary size in static equilibrium. In particular, two large black
holes can be close together without merging to form a single black hole.Comment: 23 pages, 5 figures, v2: few comments on stability modifie
The AdS/CFT Correspondence and a New Positive Energy Conjecture for General Relativity
We examine the AdS/CFT correspondence when the gauge theory is considered on
a compactified space with supersymmetry breaking boundary conditions. We find
that the corresponding supergravity solution has a negative energy, in
agreement with the expected negative Casimir energy in the field theory.
Stability of the gauge theory would imply that this supergravity solution has
minimum energy among all solutions with the same boundary conditions. Hence we
are lead to conjecture a new positive energy theorem for asymptotically locally
Anti-de Sitter spacetimes. We show that the candidate minimum energy solution
is stable against all quadratic fluctuations of the metric.Comment: 25 pages, harvma
Anti-de Sitter Quotients, Bubbles of Nothing, and Black Holes
In 3+1 dimensions there are anti-de quotients which are black holes with
toroidal event horizons. By analytic continuation of the Schwarzschild-anti-de
Sitter solution (and appropriate identifications) one finds two one parameter
families of spacetimes that contain these quotient black holes. One of these
families consists of B-metrics ("bubbles of nothing"), the other of black hole
spacetimes. All of them have vanishing conserved charges.Comment: 14 pages, 3 figures. References added, one explanation improve
Einstein gravity as a 3D conformally invariant theory
We give an alternative description of the physical content of general
relativity that does not require a Lorentz invariant spacetime. Instead, we
find that gravity admits a dual description in terms of a theory where local
size is irrelevant. The dual theory is invariant under foliation preserving
3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume
(for the spatially compact case). Locally, this symmetry is identical to that
of Horava-Lifshitz gravity in the high energy limit but our theory is
equivalent to Einstein gravity. Specifically, we find that the solutions of
general relativity, in a gauge where the spatial hypersurfaces have constant
mean extrinsic curvature, can be mapped to solutions of a particular gauge
fixing of the dual theory. Moreover, this duality is not accidental. We provide
a general geometric picture for our procedure that allows us to trade foliation
invariance for conformal invariance. The dual theory provides a new proposal
for the theory space of quantum gravity.Comment: 27 pages. Published version (minor changes and corrections
The structure of the extreme Schwarzschild-de Sitter space-time
The extreme Schwarzschild-de Sitter space-time is a spherically symmetric
solution of Einstein's equations with a cosmological constant Lambda and mass
parameter m>0 which is characterized by the condition that 9 Lambda m^2=1. The
global structure of this space-time is here analyzed in detail. Conformal and
embedding diagrams are constructed, and synchronous coordinates which are
suitable for a discussion of the cosmic no-hair conjecture are presented. The
permitted geodesic motions are also analyzed. By a careful investigation of the
geodesics and the equations of geodesic deviation, it is shown that specific
families of observers escape from falling into the singularity and approach
nonsingular asymptotic regions which are represented by special "points" in the
complete conformal diagram. The redshift of signals emitted by particles which
fall into the singularity, as detected by those observers which escape, is also
calculated.Comment: 19 pages, 10 figures, LaTeX, to appear in Gen. Rel. Gra
Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities
We study the application of the Augmented Lagrangian Method to the solution
of linear ill-posed problems. Previously, linear convergence rates with respect
to the Bregman distance have been derived under the classical assumption of a
standard source condition. Using the method of variational inequalities, we
extend these results in this paper to convergence rates of lower order, both
for the case of an a priori parameter choice and an a posteriori choice based
on Morozov's discrepancy principle. In addition, our approach allows the
derivation of convergence rates with respect to distance measures different
from the Bregman distance. As a particular application, we consider sparsity
promoting regularization, where we derive a range of convergence rates with
respect to the norm under the assumption of restricted injectivity in
conjunction with generalized source conditions of H\"older type
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