Black hole solutions in 2+1 dimensions

We give circularly symmetric solutions for null fluid collapse in 2+1-dimensional Einstein gravity with a cosmological constant. The fluid pressure $P$ and energy density $\rho$ are related by $P=k\rho$ $(k\le 1)$. The long time limit of the solutions are black holes whose horizon structures depend on the value of $k$. The $k=1$ solution is the Banados-Teitelboim-Zanelli black hole metric in the long time static limit, while the $k<1$ solutions give other, `hairy' black hole metrics in this limit.Comment: 8 pages, RevTeX (to appear in Phys. Rev. D) References to Mann and Ross, and Mann, Chan and Chan adde

Chern-Simons Gravity and Holographic Anomalies

We present a holographic treatment of Chern-Simons (CS) gravity theories in odd dimensions. We construct the associated holographic stress tensor and calculate the Weyl anomalies of the dual CFT.Comment: Added references, and minor corrections. 21 pages, havmac, no figure

Graphene and the Zermelo Optical Metric of the BTZ Black Hole

It is well known that the low energy electron excitations of the curved graphene sheet $\Sigma$ are solutions of the massless Dirac equation on a 2+1 dimensional ultra-static metric on ${\Bbb R} \times \Sigma$. An externally applied electric field on the graphene sheet induces a gauge potential which could be mimicked by considering a stationary optical metric of the Zermelo form, which is conformal to the BTZ black hole when the sheet has a constant negative curvature. The Randers form of the metric can model a magnetic field, which is related by a boost to an electric one in the Zermelo frame. We also show that there is fundamental geometric obstacle to obtaining a model that extends all the way to the black hole horizon.Comment: 10 pages Latex, no figures, substantial revisions, relation between magnetic and electric fields and Randers and Zermelo forms clarifie

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 $OSp(1|\,2;R)$ 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

Charged Rotating BTZ Black Hole and Thermodynamic Behavior of Field Equations at its Horizon

In this paper, we study different cases of the charged rotating BTZ black hole with reference to their horizons. For the existence of these cases conditions on mass, charge and angular momentum of the black hole are obtained. It is also shown that the Einstein field equations for the charged rotating BTZ black hole at the horizon can be expressed as first law of thermodynamics, $dE=TdS+\Omega dJ+\Phi dq+P_{r}dA$.Comment: 12 pages, 3 figure

Integrability of the N-body problem in (2+1)-AdS gravity

We derive a first order formalism for solving the scattering of point sources in (2+1) gravity with negative cosmological constant. We show that their physical motion can be mapped, with a polydromic coordinate transformation, to a trivial motion, in such a way that the point sources move as time-like geodesics (in the case of particles) or as space-like geodesics (in the case of BTZ black holes) of a three-dimensional hypersurface immersed in a four-dimensional Minkowskian space-time, and that the two-body dynamics is solved by two invariant masses, whose difference is simply related to the total angular momentum of the system.Comment: 15 pages, LaTeX, no figure

Graviton n-point functions for UV-complete theories in Anti-de Sitter space

We calculate graviton n-point functions in an anti-de Sitter black brane background for effective gravity theories whose linearized equations of motion have at most two time derivatives. We compare the n-point functions in Einstein gravity to those in theories whose leading correction is quadratic in the Riemann tensor. The comparison is made for any number of gravitons and for all physical graviton modes in a kinematic region for which the leading correction can significantly modify the Einstein result. We find that the n-point functions of Einstein gravity depend on at most a single angle, whereas those of the corrected theories may depend on two angles. For the four-point functions, Einstein gravity exhibits linear dependence on the Mandelstam variable s versus a quadratic dependence on s for the corrected theory.Comment: 29 page

Three-Dimensional Gravity with Conformal Scalar and Asymptotic Virasoro Algebra

Strominger has derived the Bekenstein-Hawking entropy of the BTZ black hole using asymptotic Virasoro algebra. We apply Strominger's method to a black hole solution found by Martinez and Zanelli (MZ). This is a solution of three-dimensional gravity with a conformal scalar field. The solution is not $AdS_3$, but it is asymptotically $AdS_3$; therefore, it has the asymptotic Virasoro algebra. We compute the central charge for the theory and compares Cardy's formula with the Bekenstein-Hawking entropy. It turns out that the functional form does agree, but the overall numerical coefficient does not. This is because this approach gives the "maximum possible entropy" for the numerical coefficient.Comment: 26 pages, LaTeX; v2: minor correction

The Geometrodynamics of Sine-Gordon Solitons

The relationship between N-soliton solutions to the Euclidean sine-Gordon equation and Lorentzian black holes in Jackiw-Teitelboim dilaton gravity is investigated, with emphasis on the important role played by the dilaton in determining the black hole geometry. We show how an N-soliton solution can be used to construct ``sine-Gordon'' coordinates for a black hole of mass M, and construct the transformation to more standard ``Schwarzchild-like'' coordinates. For N=1 and 2, we find explicit closed form solutions to the dilaton equations of motion in soliton coordinates, and find the relationship between the soliton parameters and the black hole mass. Remarkably, the black hole mass is non-negative for arbitrary soliton parameters. In the one-soliton case the coordinates are shown to cover smoothly a region containing the whole interior of the black hole as well as a finite neighbourhood outside the horizon. A Hamiltonian analysis is performed for slicings that approach the soliton coordinates on the interior, and it is shown that there is no boundary contribution from the interior. Finally we speculate on the sine-Gordon solitonic origin of black hole statistical mechanics.Comment: Latex, uses epsf, 30 pages, 6 figures include