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

Aspects of analyticity

CONTENTS: 1 Introduction 2 Analytic Manifolds and Analytic Continuation of Metrics 3 Walker's Spacetimes and their Maximal Extension 4 Global Structure of de Sitter and Reissner-Nordstr\"om-de Sitter Cosmos 4.1 Special Cases 4.2 Collapsing Dust 5 Euclidean Metrics 6 Physical Interpretation of Euclidean Solutions, and a remark about the Gravitational Action 6.1 Thermal Interpretation 6.2 Tunneling Interpretation 7 The Multi-Black-Hole Solutions 7.1 Merging Black Holes 7.2 Continuing Beyond the Horizons 8 Naked Singularities? Reference

Collapse of Kaluza-Klein Bubbles

Kaluza-Klein theory admits ``bubble" configurations, in which the circumference of the fifth dimension shrinks to zero on some compact surface. A three parameter family of such bubble initial data at a moment of time-symmetry (some including a magnetic field) has been found by Brill and Horowitz, generalizing the (zero-energy) ``Witten bubble" solution. Some of these data have negative total energy. We show here that all the negative energy bubble solutions start out expanding away from the moment of time symmetry, while the positive energy bubbles can start out either expanding or contracting. Thus it is unlikely that the negative energy bubbles would collapse and produce a naked singularity.Comment: 6 pages, plain LaTeX, UMDGR-94-08

Splitting of an extremal Reissner-Nordström throat via quantum tunneling

The interior near the horizon of an extremal Reissner-Nordstr\"om black hole is taken as an initial state for quantum mechanical tunneling. An instanton is presented that connects this state with a final state describing the presence of several horizons. This is interpreted as a WKB description of fluctuations due to the throat splitting into several components

Brane World in a Topological Black Hole Bulk

We consider a static brane in the background of a topological black hole, in arbitrary dimensions. For hyperbolic horizons, we find a solution only when the black hole mass assumes its minimum negative value. In this case, the tension of the brane vanishes, and the brane position coincides with the location of the horizon. For an elliptic horizon, we show that the massless mode of Randall-Sundrum is recovered in the limit of large black hole mass.Comment: Latex, 8 pages, v2: Additional references, to appear in MPL

Gauge Invariant Effective Stress-Energy Tensors for Gravitational Waves

It is shown that if a generalized definition of gauge invariance is used, gauge invariant effective stress-energy tensors for gravitational waves and other gravitational perturbations can be defined in a much larger variety of circumstances than has previously been possible. In particular it is no longer necessary to average the stress-energy tensor over a region of spacetime which is larger in scale than the wavelengths of the waves and it is no longer necessary to restrict attention to high frequency gravitational waves.Comment: 11 pages, RevTe

Perturbative Analysis of the Two-body Problem in (2+1)-AdS gravity

We derive a perturbative scheme to treat the interaction between point sources and AdS-gravity. The interaction problem is equivalent to the search of a polydromic mapping $X^A= X^A(x^\mu)$, endowed with 0(2,2) monodromies, between the physical coordinate system and a Minkowskian 4-dimensional coordinate system, which is however constrained to live on a hypersurface. The physical motion of point sources is therefore mapped to a geodesic motion on this hypersuface. We impose an instantaneous gauge which induces a set of equations defining such a polydromic mapping. Their consistency leads naturally to the Einstein equations in the same gauge. We explore the restriction of the monodromy group to O(2,1), and we obtain the solution of the fields perturbatively in the cosmological constant.Comment: 19 pages, no figures, LaTeX fil

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