260 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
Dynamics of Asymptotic Diffeomorphisms in (2+1)-Dimensional Gravity
In asymptotically anti-de Sitter gravity, diffeomorphisms that change the
conformal boundary data can be promoted to genuine physical degrees of freedom.
I show that in 2+1 dimensions, the dynamics of these degrees of freedom is
described by a Liouville action, with the correct central charge to reproduce
the entropy of the BTZ black hole.Comment: 8 pages, LaTeX; v2: slightly expanded discussion of implications,
more references; v3: more explicit comparison to Chern-Simons approach and
discussion of role of constraints; v4: added discussion of relationships to
and differences with earlier work, new and corrected reference
The lightcone of G\"odel-like spacetimes
A study of the lightcone of the G\"odel universe is extended to the so-called
G\"odel-like spacetimes. This family of highly symmetric 4-D Lorentzian spaces
is defined by metrics of the form ,
together with the requirement of spacetime homogeneity, and includes the
G\"odel metric. The quasi-periodic refocussing of cone generators with
startling lens properties, discovered by Ozsv\'{a}th and Sch\"ucking for the
lightcone of a plane gravitational wave and also found in the G\"odel universe,
is a feature of the whole G\"odel family. We discuss geometrical properties of
caustics and show that (a) the focal surfaces are two-dimensional null surfaces
generated by non-geodesic null curves and (b) intrinsic differential invariants
of the cone attain finite values at caustic subsets.Comment: 19 pages, 1 figur
Chronology protection in stationary three-dimensional spacetimes
We study chronology protection in stationary, rotationally symmetric
spacetimes in 2+1 dimensional gravity, focusing especially on the case of
negative cosmological constant. We show that in such spacetimes closed timelike
curves must either exist all the way to the boundary or, alternatively, the
matter stress tensor must violate the null energy condition in the bulk. We
also show that the matter in the closed timelike curve region gives a negative
contribution to the conformal weight from the point of view of the dual
conformal field theory. We illustrate these properties in a class of examples
involving rotating dust in anti-de Sitter space, and comment on the use of the
AdS/CFT correspondence to study chronology protection.Comment: 20 pages. V2: minor corrections, Outlook expanded, references added,
published versio
Holography and the Polyakov action
In two dimensional conformal field theory the generating functional for
correlators of the stress-energy tensor is given by the non-local Polyakov
action associated with the background geometry. We study this functional
holographically by calculating the regularized on-shell action of
asymptotically AdS gravity in three dimensions, associated with a specified
(but arbitrary) boundary metric. This procedure is simplified by making use of
the Chern-Simons formulation, and a corresponding first-order expansion of the
bulk dreibein, rather than the metric expansion of Fefferman and Graham. The
dependence of the resulting functional on local moduli of the boundary metric
agrees precisely with the Polyakov action, in accord with the AdS/CFT
correspondence. We also verify the consistency of this result with regard to
the nontrivial transformation properties of bulk solutions under Brown-Henneaux
diffeomorphisms.Comment: 20 pages, RevTeX, v2: minor typos corrected and references adde
On Holomorphic Factorization in Asymptotically AdS 3D Gravity
This paper studies aspects of ``holography'' for Euclidean signature pure
gravity on asymptotically AdS 3-manifolds. This theory can be described as
SL(2,C) CS theory. However, not all configurations of CS theory correspond to
asymptotically AdS 3-manifolds. We show that configurations that do have the
metric interpretation are parameterized by the so-called projective structures
on the boundary. The corresponding asymptotic phase space is shown to be the
cotangent bundle over the Schottky space of the boundary. This singles out a
``gravitational'' sector of the SL(2,C) CS theory. It is over this sector that
the path integral has to be taken to obtain the gravity partition function. We
sketch an argument for holomorphic factorization of this partition function.Comment: 32+1 pages, no figures; (v2) one reference added, a statement
regarding priorities modified; (v3) presentational changes, an important sign
mistake correcte
Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves
We prove that M-theory plane waves with extra supersymmetries are necessarily
homogeneous (but possibly time-dependent), and we show by explicit construction
that such time-dependent plane waves can admit extra supersymmetries. To that
end we study the Penrose limits of Goedel-like metrics, show that the Penrose
limit of the M-theory Goedel metric (with 20 supercharges) is generically a
time-dependent homogeneous plane wave of the anti-Mach type, and display the
four extra Killings spinors in that case. We conclude with some general remarks
on the Killing spinor equations for homogeneous plane waves.Comment: 20 pages, LaTeX2
Godel-type Universes in String-inspired Charged Gravity
We consider a string-inspired, gravitational theory of scalar and
electromagnetic fields and we investigate the existence of axially-symmetric,
G\"{o}del-type cosmological solutions. The neutral case is studied first and an
"extreme" G\"{o}del-type rotating solution, that respects the causality, is
determined. The charged case is considered next and two new configurations for
the, minimally-coupled to gravity, electromagnetic field are presented. Another
configuration motivated by the expected distribution of currents and charges in
a rotating universe is studied and shown to lead to a G\"{o}del-type solution
for a space-dependent coupling function. Finally, we investigate the existence
of G\"{o}del-type cosmological solutions in the framework of the one-loop
corrected superstring effective action and we determine the sole configuration
of the electromagnetic field that leads to such a solution. It turns out that,
in all the charged cases considered, Closed Timelike Curves do appear and the
causality is always violated.Comment: 26 pages, LaTex file, a few comments and references added, version to
appear in Physical Review
Cosmology in three dimensions: steps towards the general solution
We use covariant and first-order formalism techniques to study the properties
of general relativistic cosmology in three dimensions. The covariant approach
provides an irreducible decomposition of the relativistic equations, which
allows for a mathematically compact and physically transparent description of
the 3-dimensional spacetimes. Using this information we review the features of
homogeneous and isotropic 3-d cosmologies, provide a number of new solutions
and study gauge invariant perturbations around them. The first-order formalism
is then used to provide a detailed study of the most general 3-d spacetimes
containing perfect-fluid matter. Assuming the material content to be dust with
comoving spatial 2-velocities, we find the general solution of the Einstein
equations with non-zero (and zero) cosmological constant and generalise known
solutions of Kriele and the 3-d counterparts of the Szekeres solutions. In the
case of a non-comoving dust fluid we find the general solution in the case of
one non-zero fluid velocity component. We consider the asymptotic behaviour of
the families of 3-d cosmologies with rotation and shear and analyse their
singular structure. We also provide the general solution for cosmologies with
one spacelike Killing vector, find solutions for cosmologies containing scalar
fields and identify all the PP-wave 2+1 spacetimes.Comment: 35 pages, 2 figure
Holographic Protection of Chronology in Universes of the Godel Type
We analyze the structure of supersymmetric Godel-like cosmological solutions
of string theory. Just as the original four-dimensional Godel universe, these
solutions represent rotating, topologically trivial cosmologies with a
homogeneous metric and closed timelike curves. First we focus on
"phenomenological" aspects of holography, and identify the preferred
holographic screens associated with inertial comoving observers in Godel
universes. We find that holography can serve as a chronology protection agency:
The closed timelike curves are either hidden behind the holographic screen, or
broken by it into causal pieces. In fact, holography in Godel universes has
many features in common with de Sitter space, suggesting that Godel universes
could represent a supersymmetric laboratory for addressing the conceptual
puzzles of de Sitter holography. Then we initiate the investigation of
"microscopic" aspects of holography of Godel universes in string theory. We
show that Godel universes are T-dual to pp-waves, and use this fact to generate
new Godel-like solutions of string and M-theory by T-dualizing known
supersymmetric pp-wave solutions.Comment: 35 pages, 5 figures. v2: typos corrected, references adde
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