Kristin Schleich

Topological Censorship and Higher Genus Black Holes

Motivated by recent interest in black holes whose asymptotic geometry approaches that of anti‐de Sitter spacetime, we give a proof of topological censorship applicable to spacetimes with such asymptotic behavior. Employing a useful rephrasing of topological censorship as a property of homotopies of arbitrary loops, we then explore the consequences of topological censorship for the horizon topology of black holes. We find that the genera of horizons are controled by the genus of the space at infinity. Our results make it clear that there is no conflict between topological censorship and the nonspherical horizon topologies of locally anti‐de Sitter black holes. More specifically, letD be the domain of outer communications of a boundary at infinity ‘‘scri.’’ We show that the principle of topological censorship ~PTC!, which is that every causal curve in D having end points on scri can be deformed to scri, holds under reasonable conditions for timelike scri, as it is known to do for a simply connected null scri. We then show that the PTC implies that the fundamental group of scri maps, via inclusion, onto the fundamental group of D: i.e., every loop in D is homotopic to a loop in scri. We use this to determine the integral homology of preferred spacelike hypersurfaces ~Cauchy surfaces or analogues thereof! in the domain of outer communications of any four-dimensional spacetime obeying the PTC. From this, we establish that the sum of the genera of the cross sections in which such a hypersurface meets black hole horizons is bounded above by the genus of the cut of infinity defined by the hypersurface. Our results generalize familiar theorems valid for asymptotically flat spacetimes requiring simple connectivity of the domain of outer communications and spherical topology for stationary and evolving black holes. @S0556-2821~99!08218-1#

Phase transitions for flat anti-de Sitter black holes.

We reexamine the thermodynamics of anti-de Sitter (adS) black holes with Ricci flat horizons using the adS soliton as the thermal background. We find that there is a phase transition which is dependent not only on the temperature but also on the black hole area, which is an independent parameter. As in the spherical adS black hole, this phase transition is related via the adS/conformal-field-theory correspondence to a confinement-deconfinement transition in the large- N gauge theory on the conformal boundary at infinity.

The AdS/CFT correspondence and topological censorship

Abstract In this Letter we consider results on topological censorship, previously obtained by the authors in Phys. Rev. D 60 (1999) 104039, in the context of the AdS/CFT correspondence. These, and further, results are used to examine the relationship of the topology of an asymptotically locally anti-de Sitter spacetime (of arbitrary dimension) to that of its conformal boundary-at-infinity (in the sense of Penrose). We also discuss the connection of these results to results in the Euclidean setting of a similar flavor obtained by Witten and Yau in Adv. Theor. Math. Phys. 3 (1999).

Phase Transitions for Flat Anti{endash}de Sitter Black Holes

We reexamine the thermodynamics of anti-de Sitter (adS) black holes with Ricci flat horizons using the adS soliton as the thermal background. We find that there is a phase transition which is dependent not only on the temperature but also on the black hole area, which is an independent parameter. As in the spherical adS black hole, this phase transition is related via the adS/conformal-field-theory correspondence to a confinement-deconfinement transition in the large- N gauge theory on the conformal boundary at infinity.

Topological Censorship[Phys. Rev. Lett. 71, 1486 (1993)]

Classically, all topologies are allowed as solutions to the Einstein equations. However, one does not observe any topological structures on medium range distance scales, that is scales that are smaller than the size of the observed universe but larger than the microscopic scales for which quantum gravity becomes important. Recently, Friedman, Schleich and Witt have proven that there is topological censorship on these medium range distance scales: the Einstein equations, locally positive energy, and local predictability of physics imply that any medium distance scale topological structures cannot be seen. More precisely, we show that the topology of physically reasonable isolated systems is shrouded from distant observers, or in other words there is a topological censorship principle.

Charged Kaluza-Klein double-black holes in five dimensions

Using a solution generating technique based on the symmetries of the dimensionally reduced Lagrangian we derive an exact solution of the Einstein-Maxwell-Dilaton field equations in five dimensions describing a system of two general nonextremally charged static Kaluza-Klein black holes with spherical horizons. We investigate some of its thermodynamic properties and we also show how to recover various known solutions, in particular, cases.

Observer-dependent horizon temperatures: a coordinate-free formulation of Hawking radiation as tunneling

We reformulate the Hamilton–Jacobi tunneling method for calculating Hawking radiation in static, spherically symmetric spacetimes by explicitly incorporating a preferred family of frames. These frames correspond to a family of observers tied to a locally static timelike Killing vector of the spacetime. This formulation separates the role of the coordinates from the choice of vacuum and thus provides a coordinate-independent formulation of the tunneling method. In addition, it clarifies the nature of certain constants and their relation to these preferred observers in the calculation of horizon temperatures. We first use this formalism to obtain the expected temperature for a static observer at finite radius in the Schwarzschild spacetime. We then apply this formalism to the Schwarzschild–de Sitter spacetime, where there is no static observer with 4-velocity equal to the static timelike Killing vector. It is shown that a preferred static observer, one whose trajectory is geodesic, measures the lowest temperature from each horizon. Furthermore, this observer measures horizon temperatures corresponding to the well-known Bousso–Hawking normalization.

On squashed black holes in Godel universes

We investigate five-dimensional rotating and charged black holes with squashed horizons in Goedel universes. The general solution was recently derived by applying a squashing transformation on the general nonextremal charged and rotating black hole in the Goedel universe found by Wu. We give a discussion of the squashed geometry and also consider its lift to ten dimensions and discuss the T-dual geometry. Finally, using the counterterms method we compute its conserved charges and explore its thermodynamics.

Generalized sums over histories for quantum gravity (II). Simplicial conifolds

Abstract This paper examines the issues involved with concretely implementing a sum over conifolds in the formulation of euclidean sums over histories for gravity. The first step in precisely formulating any sum over topological spaces is that one must have an algorithmically implementable method of generating a list of all spaces in the set to be summed over. This requirement causes well known problems in the formulation of sums over manifolds in four or more dimensions; there is no algorithmic method of determining whether or not a topological space is an n-manifold in five or more dimensions and the issue of whether or not such an algorithm exists is open in four. However, as this paper shows, conifolds are algorithmically decidable in four dimensions. Thus the set of 4-conifolds provides a starting point for a concrete implementation of euclidean sums over histories in four dimensions. Explicit algorithms for summing over various sets of 4-conifolds are presented in the context of Regge calculus.

The exponential law: Monopole detectors, Bogoliubov transformations, and the thermal nature of the Euclidean vacuum in RP3 de Sitter spacetime

We consider scalar field theory on the 3 de Sitter spacetime (3dS), which is locally isometric to de Sitter space (dS) but has spatial topology 3. We compare the Euclidean vacua on 3dS and dS in terms of three quantities that are relevant for an inertial observer: (a) the stress-energy tensor; (b) the response of an inertial monopole particle detector; (c) the expansion of the Euclidean vacuum in terms of many-particle states associated with static coordinates centred at an inertial worldline. In all these quantities, the differences between 3dS and dS turn out to fall off exponentially at early and late proper times along the inertial trajectory. In particular, (b) and (c) yield at early and late proper times in 3dS the usual thermal result for the de Sitter Hawking temperature. This conforms to what one might call an exponential law: in expanding locally de Sitter spacetimes, differences due to global topology should fall off exponentially in the proper time.