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

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

Quantum scalar field on three-dimensional (BTZ) black hole instanton: heat kernel, effective action and thermodynamics

We consider the behaviour of a quantum scalar field on three-dimensional Euclidean backgrounds: Anti-de Sitter space, the regular BTZ black hole instanton and the BTZ instanton with a conical singularity at the horizon. The corresponding heat kernel and effective action are calculated explicitly for both rotating and non-rotating holes. The quantum entropy of the BTZ black hole is calculated by differentiating the effective action with respect to the angular deficit at the conical singularity. The renormalization of the UV-divergent terms in the action and entropy is considered. The structure of the UV-finite term in the quantum entropy is of particular interest. Being negligible for large outer horizon area $A_+$ it behaves logarithmically for small $A_+$. Such behaviour might be important at late stages of black hole evaporation.Comment: 28 pages, latex, 2 figures now include

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.

An Equivalence Between Momentum and Charge in String Theory

It is shown that for a translationally invariant solution to string theory, spacetime duality interchanges the momentum in the symmetry direction and the axion charge per unit length. As one application, we show explicitly that charged black strings are equivalent to boosted (uncharged) black strings. The extremal black strings (which correspond to the field outside of a fundamental macroscopic string) are equivalent to plane fronted waves describing strings moving at the speed of light.Comment: 10 page

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

On classical super-radiance in Kerr-Newman-anti-de Sitter black holes

We study in detail the modes of a classical scalar field on a Kerr-Newman-anti-de Sitter (KN-AdS) black hole. We construct sets of basis modes appropriate to the two possible boundary conditions (``reflective'' and ``transparent'') at time-like infinity, and consider whether super-radiance is possible. If we employ ``reflective'' boundary conditions, all modes are non-super-radiant. On the other hand, for ``transparent'' boundary conditions, the presence of super-radiance depends on our definition of positive frequency. For those KN-AdS black holes having a globally time-like Killing vector, the natural choice of positive frequency leads to no super-radiance. For other KN-AdS black holes, there is a choice of positive frequency which gives no super-radiance, but for other choices there will, in general, be super-radiance.Comment: 23 pages, 3 figures, v2: minor changes, references adde

Quantum Scalar Field on the Massless (2+1)-Dimensional Black Hole Background

The behavior of a quantum scalar field is studied in the metric ground state of the (2+1)-dimensional black hole of Ba\~nados, Teitelboim and Zanelli which contains a naked singularity. The one-loop BTZ partition function and the associate black hole effective entropy, the expectation value of the quantum fluctuation as well as the renormalized expectation value of the stress tensor are explicitly computed in the framework of the $\zeta$-function procedure. This is done for all values of the coupling with the curvature, the mass of the field and the temperature of the quantum state. In the massless conformally coupled case, the found stress tensor is used for determining the quantum back reaction on the metric due to the scalar field in the quantum vacuum state, by solving the semiclassical Einstein equations. It is finally argued that, within the framework of the 1/N expansion, the Cosmic Censorship Hypothesis is implemented since the naked singularity of the ground state metric is shielded by an event horizon created by the back reaction.Comment: 18 pages, RevTeX, no figures, minor changes, final version accepted for publication in Phys. Rev.

On the Classical Stability of Orientifold Cosmologies

We analyze the classical stability of string cosmologies driven by the dynamics of orientifold planes. These models are related to time-dependent orbifolds, and resolve the orbifold singularities which are otherwise problematic by introducing orientifold planes. In particular, we show that the instability discussed by Horowitz and Polchinski for pure orbifold models is resolved by the presence of the orientifolds. Moreover, we discuss the issue of stability of the cosmological Cauchy horizon, and we show that it is stable to small perturbations due to in-falling matter.Comment: 40 pages, 13 figures. Reference and conclusion added. Published versio