arXiv subjects

Robert B. Mann

Publications and source records attributed to Robert B. Mann.

352 records · Page 20Linked to original sources

arXiv2004

Dynamical Charged N-body Equilibrium in Circular Dilaton Gravity

We extend the problem of $(1+1)$ circular dilaton gravity to include charged particles. We examine the two (charged) particle case in detail and find an exact equilibrium solution. We then extend this to $N-$particles and obtain a solution for this case as well. This class of solutions corresponds to $N$-particles of the same mass, spaced evenly around the circle with charges chosen so that the electric field satisfies $E^{2}=$constant. We discuss the relation of these solutions to the previous uncharged equilibrium solutions and examine the behavior when the number of particles is large. We comment on the challenges in further generalizing the solutions we obtain.

gr-qc↗

arXiv2000

Conserved Quantities in Kerr-anti-de Sitter Spacetimes in Various Dimensions

We compute the conserved charges for Kerr anti-de Sitter spacetimes in various dimensions using the conformal and the counterterm prescriptions. We show that the conserved charge corresponding to the global timelike killing vector computed by the two methods differ by a constant dependent on the rotation parameter and cosmological constant in odd spacetime dimensions, whereas the charge corresponding to the rotational killing vector is the same in either approach. We comment on possible implications of our results to the AdS/CFT correspondence.

hep-th↗

arXiv1998

Universality of Quantum Entropy for Extreme Black Holes

We consider the extremal limit of a black hole geometry of the Reissner-Nordstrom type and compute the quantum corrections to its entropy. Universally, the limiting geometry is the direct product of two 2-dimensional spaces and is characterized by just a few parameters. We argue that the quantum corrections to the entropy of such extremal black holes due to a massless scalar field have a universal behavior. We obtain explicitly the form of the quantum entropy in this extremal limit as function of the parameters of the limiting geometry. We generalize these results to black holes with toroidal or higher genus horizon topologies. In general, the extreme quantum entropy is completely determined by the spectral geometry of the horizon and in the ultra-extreme case it is just a determinant of the 2-dimensional Laplacian. As a byproduct of our considerations we obtain expressions for the quantum entropy of black holes which are not of the Reissner-Nordstrom type: the extreme dilaton and extreme Kerr-Newman black holes. In both cases the classical Bekenstein-Hawking entropy is modified by logarithmic corrections.

hep-th↗

arXiv1997

Entropy of Constant Curvature Black Holes in General Relativity

We consider the thermodynamic properties of the constant curvature black hole solution recently found by Banados. We show that it is possible to compute the entropy and the quasilocal thermodynamics of the spacetime using the Einstein-Hilbert action of General Relativity. The constant curvature black hole has some unusual properties which have not been seen in other black hole spacetimes. The entropy of the black hole is not associated with the event horizon; rather it is associated with the region between the event horizon and the observer. Further, surfaces of constant internal energy are not isotherms so the first law of thermodynamics exists only in an integral form. These properties arise from the unusual topology of the Euclidean black hole instanton.

gr-qc↗

arXiv1996

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.

hep-th↗

arXiv1996

Conical geometry and quantum entropy of a charged Kerr black hole

We apply the method of conical singularities to calculate the tree-level entropy and its one-loop quantum corrections for a charged Kerr black hole. The Euclidean geometry for the Kerr-Newman metric is considered. We show that for an arbitrary periodization in Euclidean space there exists a conical singularity at the horizon. Its $δ$-function like curvatures are calculated and are shown to behave similar to the static case. The heat kernel expansion for a scalar field on this conical space background is derived and the (divergent) quantum correction to the entropy is obtained. It is argued that these divergences can be removed by renormalization of couplings in the tree-level gravitational action in a manner similar to that for a static black hole.

hep-th↗

arXiv1995

Spinning Black Holes in (2+1)-dimensional String and Dilaton Gravity

We present a new class of spinning black hole solutions in $(2+1)$-dimensional general relativity minimally coupled to a dilaton with potential $e^{bϕ}Λ$. When $b=4$, the corresponding spinning black hole is a solution of low energy $(2+1)$-dimensional string gravity. Apart from the limiting case of the $BTZ$ black hole, these spinning black holes have no inner horizon and a curvature singularity only at the origin. We compute the mass and angular momentum parameters of the solutions at spatial infinity, as well as their temperature and entropy.

gr-qc↗

arXiv1995

Charged Dilaton Black Holes with Unusual Asymptotics

We present a new class of black hole solutions in Einstein-Maxwell-dilaton gravity in $n \ge 4$ dimensions. These solutions have regular horizons and a singularity only at the origin. Their asymptotic behavior is neither asymptotically flat nor (anti-) de Sitter. Similar solutions exist for certain Liouville-type potentials for the dilaton.

gr-qc↗

arXiv1992

Gauge Formulation of the Spinning Black Hole in (2+1)-Dimensional Anti-de Sitter Space

We compute the group element of SO(2,2) associated with the spinning black hole found by Bañados, Teitelboim and Zanelli in (2+1)-dimensional anti-de Sitter space-time. We show that their metric is built with SO(2,2) gauge invariant quantities and satisfies Einstein's equations with negative cosmological constant everywhere except at $r=0$. Moreover, although the metric is singular on the horizons, the group element is continuous and possesses a kink there.

gr-qc↗

arXiv1992

The Causal Structure of Two-Dimensional Spacetimes

We investigate the causal structure of $(1+1)$-dimensional spacetimes. For two sets of field equations we show that at least locally any spacetime is a solution for an appropriate choice of the matter fields. For the theories under consideration we investigate how smoothness of their black hole solutions affects time orientation. We show that if an analog to Hawking's area theorem holds in two spacetime dimensions, it must actually state that the size of a black hole never {\em increases}, contrary to what happens in four dimensions. Finally, we discuss the applicability of the Penrose and Hawking singularity theorems to two spacetime dimensions.

hep-th↗