Lattice Universes in 2+1-dimensional gravity

Lattice universes are spatially closed space-times of spherical topology in the large, containing masses or black holes arranged in the symmetry of a regular polygon or polytope. Exact solutions for such spacetimes are found in 2+1 dimensions for Einstein gravity with a non-positive cosmological constant. By means of a mapping that preserves the essential nature of geodesics we establish analogies between the flat and the negative curvature cases. This map also allows treatment of point particles and black holes on a similar footing.Comment: 14 pages 7 figures, to appear in Festschrift for Vince Moncrief (CQG

Vanishing of the conformal anomaly for strings in a gravitational wave

Using the non-symmetric-connection approach proposed by Osborn, we demonstrate that, for a bosonic string in a specially chosen plane-fronted gravitational wave and an axion background, the conformal anomaly vanishes at the two-loop level. Under some conditions, the anomaly vanishes at all orders.Comment: Previously not available in hep-th. Published as Physics Letters B 313, 10 (1993). Plain TeX 6 pages. No figure

Back-reaction of a conformal field on a three-dimensional black hole

The first order corrections to the geometry of the (2+1)-dimensional black hole due to back-reaction of a massless conformal scalar field are computed. The renormalized stress energy tensor used as the source of Einstein equations is computed with the Green function for the black-hole background with transparent boundary conditions. This tensor has the same functional form as the one found in the nonperturbative case which can be exactly solved. Thus, a static, circularly symmetric and asymptotically anti-de Sitter black hole solution of the semiclassical equations is found. The corrections to the thermodynamic quantities are also computed.Comment: 12 pages, RevTeX, no figure

Curvature singularity of the distributional BTZ black hole geometry

For the non-rotating BTZ black hole, the distributional curvature tensor field is found. It is shown to have singular parts proportional to a $\delta$-distribution with support at the origin. This singularity is related, through Einstein field equations, to a point source. Coordinate invariance and independence on the choice of differentiable structure of the results are addressed.Comment: Latex, 7 page

Gott Time Machines, BTZ Black Hole Formation, and Choptuik Scaling

We study the formation of BTZ black holes by the collision of point particles. It is shown that the Gott time machine, originally constructed for the case of vanishing cosmological constant, provides a precise mechanism for black hole formation. As a result, one obtains an exact analytic understanding of the Choptuik scaling.Comment: 6 pages, Late

Form factors at strong coupling via a Y-system

We compute form factors in planar N=4 Super Yang-Mills at strong coupling. Namely we consider the overlap between an operator insertion and 2n gluons. Through the gauge/string duality these are given by minimal surfaces in AdS space. The surfaces end on an infinite periodic sequence of null segments at the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We derive set of functional equations for the cross ratios as functions of the spectral parameter. These equations are of the form of a Y-system. The integral form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by the free energy of the TBA system or critical value of Yang-Yang functional. We consider a restricted set of operators which have small conformal dimension

Interior Structure of a Charged Spinning Black Hole in (2+1)(2+1)-Dimensions

The phenomenon of mass inflation is shown to occur for a rotating black hole. We demonstrate this feature in $(2+1)$ dimensions by extending the charged spinning BTZ black hole to Vaidya form. We find that the mass function diverges in a manner quantitatively similar to its static counterparts in $(3+1)$, $(2+1)$ and $(1+1)$ dimensions.Comment: 5 pages, 2 figures (appended as postscript files), WATPHYS-TH94/0

Thermodynamics and Evaporation of the 2+1-D Black Hole

The properties of canonical and microcanonical ensembles of a black hole with thermal radiation and the problem of black hole evaporation in 3-D are studied. In 3-D Einstein-anti-de Sitter gravity we have two relevant mass scales, $m_c=1/G$, and $m_p=(\hbar^2\Lambda/G)^{1/3}$, which are particularly relevant for the evaporation problem. It is argued that in the `weak coupling' regime $\Lambda<(\hbar G)^{-2}$, the end point of an evaporating black hole formed with an initial mass $m_0>m_p$, is likely to be a stable remnant in equilibrium with thermal radiation. The relevance of these results for the information problem and for the issue of back reaction is discussed. In the `strong coupling' regime, $\Lambda>(\hbar G)^{-2}$ a full fledged quantum gravity treatment is required. Since the total energy of thermal states in anti-de Sitter space with reflective boundary conditions at spatial infinity is bounded and conserved, the canonical and microcanonical ensembles are well defined. For a given temperature or energy black hole states are locally stable. In the weak coupling regime black hole states are more probable then pure radiation states.Comment: 11 pages, TAUP 2141/94, Late

Gravitational collapse in 2+1 dimensional AdS spacetime

We present results of numerical simulations of the formation of black holes from the gravitational collapse of a massless, minimally-coupled scalar field in 2+1 dimensional, axially-symmetric, anti de-Sitter (AdS) spacetime. The geometry exterior to the event horizon approaches the BTZ solution, showing no evidence of scalar `hair'. To study the interior structure we implement a variant of black-hole excision, which we call singularity excision. We find that interior to the event horizon a strong, spacelike curvature singularity develops. We study the critical behavior at the threshold of black hole formation, and find a continuously self-similar solution and corresponding mass-scaling exponent of approximately 1.2. The critical solution is universal to within a phase that is related to the angle deficit of the spacetime.Comment: 31 pages, 20 figures, LaTeX. Replaced with version to be published in Phys. Rev.

The 2+1 Kepler Problem and Its Quantization

We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass frame. When the system is quantized, we find some possibly general effects of quantum gravity, such as a minimal distances and a foaminess of the spacetime at the order of the Planck length. We also obtain a quantization of geometry, which restricts the possible asymptotic geometries of the universe.Comment: 59 pages, LaTeX2e, 9 eps figure