Real Formulations of Complex Gravity and a Complex Formulation of Real Gravity

Two gauge and diffeomorphism invariant theories on the Yang-Mills phase space are studied. They are based on the Lie-algebras $so(1,3)$ and $\widetilde{so(3)}$ -- the loop-algebra of $so(3)$. Although the theories are manifestly real, they can both be reformulated to show that they describe complex gravity and an infinite number of copies of complex gravity, respectively. The connection to real gravity is given. For these theories, the reality conditions in the conventional Ashtekar formulation are represented by normal constraint-like terms.Comment: 23 pages, CGPG-94/4-

A Modular Invariant Quantum Theory From the Connection Formulation of (2+1)-Gravity on the Torus

By choosing an unconventional polarization of the connection phase space in (2+1)-gravity on the torus, a modular invariant quantum theory is constructed. Unitary equivalence to the ADM-quantization is shown.Comment: Latex, 4 page

Making Anti-de Sitter Black Holes

It is known from the work of Banados et al. that a space-time with event horizons (much like the Schwarzschild black hole) can be obtained from 2+1 dimensional anti-de Sitter space through a suitable identification of points. We point out that this can be done in 3+1 dimensions as well. In this way we obtain black holes with event horizons that are tori or Riemann surfaces of genus higher than one. They can have either one or two asymptotic regions. Locally, the space-time is isometric to anti-de Sitter space.Comment: LaTeX, 10 pages, 6 postscript figures, uses epsf.te

Black Holes and Causal Structure in Anti-de Sitter Isometric Spacetimes

The observation that the 2+1 dimensional BTZ black hole can be obtained as a quotient space of anti-de Sitter space leads one to ask what causal behaviour other such quotient spaces can display. In this paper we answer this question in 2+1 and 3+1 dimensions when the identification group has one generator. Among other things we find that there does not exist any 3+1 generalization of the rotating BTZ hole. However, the non-rotating generalization exists and exhibits some unexpected properties. For example, it turns out to be non-static and to possess a non-trivial apparent horizon.Comment: LaTeX, 22 pages, 10 postscript figures, uses epsf.te

Large Diffeomorphisms in (2+1)-Quantum Gravity on the Torus

The issue of how to deal with the modular transformations -- large diffeomorphisms -- in (2+1)-quantum gravity on the torus is discussed. I study the Chern-Simons/connection representation and show that the behavior of the modular transformations on the reduced configuration space is so bad that it is possible to rule out all finite dimensional unitary representations of the modular group on the Hilbert space of $L^2$-functions on the reduced configuration space. Furthermore, by assuming piecewise continuity for a dense subset of the vectors in any Hilbert space based on the space of complex valued functions on the reduced configuration space, it is shown that finite dimensional representations are excluded no matter what inner-product we define in this vector space. A brief discussion of the loop- and ADM-representations is also included.Comment: The proof for the nonexistence of the one- and two-dimensional representations of PSL(2,Z) in the relevant Hilbert space, has been extended to cover all finite dimensional unitary representations. The notation is slightly improved and a few references are added

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

Thermodynamics of (3+1)-dimensional black holes with toroidal or higher genus horizons

We examine counterparts of the Reissner-Nordstrom-anti-de Sitter black hole spacetimes in which the two-sphere has been replaced by a surface Sigma of constant negative or zero curvature. When horizons exist, the spacetimes are black holes with an asymptotically locally anti-de Sitter infinity, but the infinity topology differs from that in the asymptotically Minkowski case, and the horizon topology is not S^2. Maximal analytic extensions of the solutions are given. The local Hawking temperature is found. When Sigma is closed, we derive the first law of thermodynamics using a Brown-York type quasilocal energy at a finite boundary, and we identify the entropy as one quarter of the horizon area, independent of the horizon topology. The heat capacities with constant charge and constant electrostatic potential are shown to be positive definite. With the boundary pushed to infinity, we consider thermodynamical ensembles that fix the renormalized temperature and either the charge or the electrostatic potential at infinity. Both ensembles turn out to be thermodynamically stable, and dominated by a unique classical solution.Comment: 25 pages, REVTeX v3.1, contains 5 LaTeX figures. (Typos corrected, references and minor comments added. To be published in Phys. Rev. D.