32 research outputs found
A Spinning Anti-de Sitter Wormhole
We construct a 2+1 dimensional spacetime of constant curvature whose spatial
topology is that of a torus with one asymptotic region attached. It is also a
black hole whose event horizon spins with respect to infinity. An observer
entering the hole necessarily ends up at a "singularity"; there are no inner
horizons.
In the construction we take the quotient of 2+1 dimensional anti-de Sitter
space by a discrete group Gamma. A key part of the analysis proceeds by
studying the action of Gamma on the boundary of the spacetime.Comment: Latex, 28 pages, 7 postscript figures included in text, a Latex file
without figures can be found at http://vanosf.physto.se/~stefan/spinning.html
Replaced with journal version, minor change
The Anti-de Sitter Gott Universe: A Rotating BTZ Wormhole
Recently it has been shown that a 2+1 dimensional black hole can be created
by a collapse of two colliding massless particles in otherwise empty anti-de
Sitter space. Here we generalize this construction to the case of a non-zero
impact parameter. The resulting spacetime, which may be regarded as a Gott
universe in anti-de Sitter background, contains closed timelike curves. By
treating these as singular we are able to interpret our solution as a rotating
black hole, hence providing a link between the Gott universe and the BTZ black
hole. When analyzing the spacetime we see how the full causal structure of the
interior can be almost completely inferred just from considerations of the
conformal boundary.Comment: 46 pages (LaTeX2e), 13 figures (eps
Black Holes and Wormholes in 2+1 Dimensions
A large variety of spacetimes---including the BTZ black holes---can be
obtained by identifying points in 2+1 dimensional anti-de Sitter space by means
of a discrete group of isometries. We consider all such spacetimes that can be
obtained under a restriction to time symmetric initial data and one asymptotic
region only. The resulting spacetimes are non-eternal black holes with
collapsing wormhole topologies. Our approach is geometrical, and we discuss in
detail: The allowed topologies, the shape of the event horizons, topological
censorship and trapped curves.Comment: 23 pages, LaTeX, 11 figure
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
Where are the trapped surfaces?
We discuss the boundary of the spacetime region through each point of which a
trapped surface passes, first in some simple soluble examples, and then in the
self-similar Vaidya solution. For the latter the boundary must lie strictly
inside the event horizon. We present a class of closed trapped surfaces
extending strictly outside the apparent horizon.Comment: 6 pages, 1 figure; talk at the Spanish Relativity Meeting ERE09 in
Bilba
Single-exterior black holes and the AdS-CFT conjecture
In the context of the conjectured AdS-CFT correspondence of string theory, we
consider a class of asymptotically Anti-de Sitter black holes whose conformal
boundary consists of a single connected component, identical to the conformal
boundary of Anti-de Sitter space. In a simplified model of the boundary theory,
we find that the boundary state to which the black hole corresponds is pure,
but this state involves correlations that produce thermal expectation values at
the usual Hawking temperature for suitably restricted classes of operators. The
energy of the state is finite and agrees in the semiclassical limit with the
black hole mass. We discuss the relationship between the black hole topology
and the correlations in the boundary state, and speculate on generalizations of
the results beyond the simplified model theory.Comment: 27 pages, LaTeX, using REVTeX v3.1 with amsfonts and epsf, with two
eps figures. (v3: references updated
Poincare ball embeddings of the optical geometry
It is shown that optical geometry of the Reissner-Nordstrom exterior metric
can be embedded in a hyperbolic space all the way down to its outer horizon.
The adopted embedding procedure removes a breakdown of flat-space embeddings
which occurs outside the horizon, at and below the Buchdahl-Bondi limit
(R/M=9/4 in the Schwarzschild case). In particular, the horizon can be captured
in the optical geometry embedding diagram. Moreover, by using the compact
Poincare ball representation of the hyperbolic space, the embedding diagram can
cover the whole extent of radius from spatial infinity down to the horizon.
Attention is drawn to advantages of such embeddings in an appropriately curved
space: this approach gives compact embeddings and it distinguishes clearly the
case of an extremal black hole from a non-extremal one in terms of topology of
the embedded horizon.Comment: 16 pages, 8 figures; CQG accepte
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
Supersymmetric isolated horizons
We construct a covariant phase space for rotating weakly isolated horizons in
Einstein-Maxwell-Chern-Simons theory in all (odd) dimensions. In
particular, we show that horizons on the corresponding phase space satisfy the
zeroth and first laws of black-hole mechanics. We show that the existence of a
Killing spinor on an isolated horizon in four dimensions (when the Chern-Simons
term is dropped) and in five dimensions requires that the induced (normal)
connection on the horizon has to vanish, and this in turn implies that the
surface gravity and rotation one-form are zero. This means that the
gravitational component of the horizon angular momentum is zero, while the
electromagnetic component (which is attributed to the bulk radiation field) is
unconstrained. It follows that an isolated horizon is supersymmetric only if it
is extremal and nonrotating. A remarkable property of these horizons is that
the Killing spinor only has to exist on the horizon itself. It does not have to
exist off the horizon. In addition, we find that the limit when the surface
gravity of the horizon goes to zero provides a topological constraint.
Specifically, the integral of the scalar curvature of the cross sections of the
horizon has to be positive when the dominant energy condition is satisfied and
the cosmological constant is zero or positive, and in particular
rules out the torus topology for supersymmetric isolated horizons (unless
) if and only if the stress-energy tensor is of the form
such that for any two null vectors and with
normalization on the horizon.Comment: 26 pages, 1 figure; v2: typos corrected, topology arguments
corrected, discussion of black rings and dipole charge added, references
added, version to appear in Classical and Quantum Gravit