149 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
Aspects of Diffeomorphism and Conformal invariance in classical Liouville theory
The interplay between the diffeomorphism and conformal symmetries (a feature
common in quantum field theories) is shown to be exhibited for the case of
black holes in two dimensional classical Liouville theory. We show that
although the theory is conformally invariant in the near horizon limit, there
is a breaking of the diffeomorphism symmetry at the classical level. On the
other hand, in the region away from the horizon, the conformal symmetry of the
theory gets broken with the diffeomorphism symmetry remaining intact.Comment: Accepted in Euro. Phys. Letters., Title changed, abstract modified,
major modifications made in the pape
Three Dimensional Gravity From SU(2) Yang-Mills Theory in Two Dimensions
We argue that two dimensional classical SU(2) Yang-Mills theory describes the
embedding of Riemann surfaces in three dimensional curved manifolds.
Specifically, the Yang-Mills field strength tensor computes the Riemannian
curvature tensor of the ambient space in a thin neighborhood of the surface. In
this sense the two dimensional gauge theory then serves as a source of three
dimensional gravity. In particular, if the three dimensional manifold is flat
it corresponds to the vacuum of the Yang-Mills theory. This implies that all
solutions to the original Gauss-Codazzi surface equations determine two
dimensional integrable models with a SU(2) Lax pair. Furthermore, the three
dimensional SU(2) Chern-Simons theory describes the Hamiltonian dynamics of two
dimensional Riemann surfaces in a four dimensional flat space-time
The boundary field theory induced by the Chern-Simons theory
The Chern-Simons theory defined on a 3-dimensional manifold with boundary is
written as a two-dimensional field theory defined only on the boundary of the
three-manifold. The resulting theory is, essentially, the pullback to the
boundary of a symplectic structure defined on the space of auxiliary fields in
terms of which the connection one-form of the Chern-Simons theory is expressed
when solving the condition of vanishing curvature. The counting of the physical
degrees of freedom living in the boundary associated to the model is performed
using Dirac's canonical analysis for the particular case of the gauge group
SU(2). The result is that the specific model has one physical local degree of
freedom. Moreover, the role of the boundary conditions on the original Chern-
Simons theory is displayed and clarified in an example, which shows how the
gauge content as well as the structure of the constraints of the induced
boundary theory is affected.Comment: 10 page
Supergeometry of Three Dimensional Black Holes
We show how the supersymmetric properties of three dimensional black holes
can be obtained algebraically. The black hole solutions are constructed as
quotients of the supergroup by a discrete subgroup of its
isometry supergroup. The generators of the action of the isometry supergroup
which commute with these identifications are found. These yield the
supersymmetries for the black hole as found in recent studies as well as the
usual geometric isometries. It is also shown that in the limit of vanishing
cosmological constant, the black hole vacuum becomes a null orbifold, a
solution previously discussed in the context of string theory.Comment: 12 pages, harvmac, discussion of rotating black hole added, some
minor corrections, reference adde
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
Embeddings of the Virasoro algebra and black hole entropy
We consider embeddings of the Virasoro algebra into other Virasoro algebras
with different central charges. A Virasoro algebra with central charge c
(assumed to be a positive integer) and zero mode operator L_0 can be embedded
into another Virasoro algebra with central charge one and zero mode operator c
L_0. We point out that this provides a new route to investigate the black hole
entropy problem in 2+1 dimensions.Comment: 4 pages (twocolumn), latex, no figures. Reference added. To appear in
Phys.Rev.Let
Orientifolded Locally AdS3 Geometries
Continuing the analysis of [arXiv:1003.4089[hep-th]], we classify all locally
AdS3 stationary axi-symmetric unorientable solutions to AdS3 Einstein gravity
and show that they are obtained by applying certain orientifold projection on
AdS3, BTZ or AdS3 self-dual orbifold, respectively O-AdS3, O-BTZ and O-SDO
geometries. Depending on the orientifold fixed surface, the O-surface, which is
either a space-like 2D plane or cylinder, or a light-like 2D plane or cylinder
one can distinguish four distinct cases. For the space-like orientifold plane
or cylinder cases these geometries solve AdS3 Einstein equations and are hence
locally AdS3 everywhere except at the O-surface, where there is a
delta-function source. For the light-like cases the geometry is a solution to
Einstein equations even at the O-surface. We discuss the causal structure for
static, extremal and general rotating O-BTZ and O-SDO cases as well as the
geodesic motion on these geometries. We also discuss orientifolding Poincare
patch AdS3 and AdS2 geometries as a way to geodesic completion of these spaces
and comment on the 2D CFT dual to the O-geometries.Comment: 26 page, 4 .eps figure
Multi-Black-Holes in Three Dimensions
We construct time-dependent multi-centre solutions to three-dimensional
general relativity with zero or negative cosmological constant. These solutions
correspond to dynamical systems of freely falling black holes and conical
singularities, with a multiply connected spacetime topology. Stationary
multi-black-hole solutions are possible only in the extreme black hole case.Comment: 8 pages, \LaTex, 4 figures (available on request), GCR 94/02/0
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