Vacuum polarization near asymptotically anti-de Sitter black holes in odd dimensions
TL;DR: In this article, the authors derived the propagator in an exact form for a conformal scalar field in the asymptotically anti-de Sitter black hole spacetime so as to study the quantum effects of the scalar fields.
Abstract: Recently, Banados, Teitelboim and Zanelli obtained spherically symmetric black hole solutions in a particular class of Einstein--Lovelock gravity. We derive the propagator in an exact form for a conformal scalar field in the asymptotically anti-de Sitter black hole spacetime so as to study the quantum effects of the scalar fields. We treat the cases in odd dimensions in this paper. We calculate the vacuum expectation value of $\langle\varphi^2\rangle$ and show its dependence on the radial coordinate for the five-dimensional case as an example.
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TL;DR: In this paper, the perturbative effects of a quantum conformally coupled scalar field on rotating (2+1$)-dimensional black holes and naked singularities were investigated analytically.
Abstract: We analytically investigate the perturbative effects of a quantum conformally coupled scalar field on rotating ($2+1$)-dimensional black holes and naked singularities. In both cases we obtain the quantum-backreacted metric analytically. In the black hole case, we explore the quantum corrections on different regions of relevance for a rotating black hole geometry. We find that the quantum effects lead to a growth of both the event horizon and the ergosphere, as well as to a reduction of the angular velocity compared to their corresponding unperturbed values. Quantum corrections also give rise to the formation of a curvature singularity at the Cauchy horizon and show no evidence of the appearance of a superradiant instability. In the naked singularity case, quantum effects lead to the formation of a horizon that hides the conical defect, thus turning it into a black hole. The fact that these effects occur not only for static but also for spinning geometries makes a strong case for the role of quantum mechanics as a cosmic censor in Nature.
25 citations
TL;DR: In this article, the renormalized vacuum polarization for a massless, conformally coupled scalar field on asymptotically anti-de Sitter black hole backgrounds is computed.
Abstract: We compute the renormalized vacuum polarization for a massless, conformally coupled scalar field on asymptotically anti--de Sitter black hole backgrounds. Mixed (Robin) boundary conditions are applied on the spacetime boundary. We consider black holes with nonspherical event horizon topology as well as spherical event horizons. The quantum scalar field is in the Hartle-Hawking state, and we employ Euclidean methods to calculate the renormalized expectation values. Far from the black hole, we find that the vacuum polarization approaches a finite limit, which is the same for all boundary conditions except Dirichlet boundary conditions.
9 citations
TL;DR: In this article, the authors investigated quantum effects on topological black hole space-times within the framework of quantum field theory on curved space times, and extended a recent mode-sum regularization prescription for the computation of the renormalized vacuum polarization to asymptotically anti-de Sitter black holes with nonspherical event horizon topology.
Abstract: We investigate quantum effects on topological black hole space-times within the framework of quantum field theory on curved space-times. Considering a quantum scalar field, we extend a recent mode-sum regularization prescription for the computation of the renormalized vacuum polarization to asymptotically anti-de Sitter black holes with nonspherical event horizon topology. In particular, we calculate the vacuum polarization for a massless, conformally-coupled scalar field on a four-dimensional topological Schwarzschild-anti-de Sitter black hole background, comparing our results with those for a spherically-symmetric black hole.
7 citations
TL;DR: In this paper, the gravitational back-reaction of a conformally invariant scalar field within a black cosmic string interior with cosmological constant is calculated using the perturbed metric, and the gravitational effects of the quantum field are calculated.
Abstract: The gravitational back-reaction is calculated for the conformally invariant scalar field within a black cosmic string interior with cosmological constant. Using the perturbed metric, the gravitational effects of the quantum field are calculated. It is found that near the horizon, the perturbations initially strengthen the singularity. This effect is similar to the case of spherical symmetry (without a cosmological constant). This indicates that the behaviour of quantum effects may be universal and not dependent on the geometry of the spacetime or the presence of a non-zero cosmological constant.
7 citations
TL;DR: In this paper, the authors extend to higher dimensionality the methods and computations of vacuum polarization effects in black hole spacetimes and prove the cancellation of the divergences and the regularity of the vacuum polarization once counterterms are added up.
Abstract: The goal of this paper is to extend to higher dimensionality the methods and computations of vacuum polarization effects in black hole spacetimes. We focus our attention on the case of five dimensional Schwarzschild-Tangherlini black holes, for which we adapt the general method initially developed by Candelas and later refined by Anderson and others. We make use of point splitting regularization and of the WKB approximation to extract the divergences occurring in the coincidence limit of the Green function and, after calculating the counterterms using the Schwinger--De Witt expansion, we explicitly prove the cancellation of the divergences and the regularity of the vacuum polarization once counterterms are added up. We finally handle numerically the renormalized expression of the vacuum polarization. As a check on the method we also prove the regularity of the vacuum polarization in the six dimensional case in the large mass limit.
5 citations
Cites methods from "Vacuum polarization near asymptotic..."
...Reference [18] calculated the vacuum polarization outside a five dimensional AdS black hole in a modified theory of gravity....
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TL;DR: The standard Einstein-Maxwell equations in 2+1 spacetime dimensions, with a negative cosmological constant, admit a black hole solution that appears as a negative energy state separated by a mass gap from the continuous black hole spectrum.
Abstract: The standard Einstein-Maxwell equations in 2+1 spacetime dimensions, with a negative cosmological constant, admit a black hole solution. The 2+1 black hole---characterized by mass, angular momentum, and charge, defined by flux integrals at infinity---is quite similar to its 3+1 counterpart. Anti--de Sitter space appears as a negative energy state separated by a mass gap from the continuous black hole spectrum. Evaluation of the partition function yields that the entropy is equal to twice the perimeter length of the horizon.
3,640 citations
TL;DR: The geometry of the spinning black holes of standard Einstein theory in 2+1 dimensions, with a negative cosmological constant, and without couplings to matter, is analyzed in detail.
Abstract: The geometry of the spinning black holes of standard Einstein theory in 2+1 dimensions, with a negative cosmological constant, and without couplings to matter, is analyzed in detail. It is shown that the black hole arises from identifications of points of anti\char21{}de Sitter space by a discrete subgroup of SO(2,2). The generic black hole is a smooth manifold in the metric sense. The surface r=0 is not a curvature singularity but, rather, a singularity in the causal structure. Continuing past it would introduce closed timelike lines. However, simple examples show the regularity of the metric at r=0 to be unstable: couplings to matter bring in a curvature singularity there. Kruskal coordinates and Penrose diagrams are exhibited. Special attention is given to the limiting cases of (i) the spinless hole of zero mass, which differs from anti\char21{}de Sitter space and plays the role of the vacuum, and (ii) the spinning hole of maximal angular momentum. A thorough classification of the elements of the Lie algebra of SO(2,2) is given in an appendix.
1,921 citations
TL;DR: In this paper, a covariant geodesic point separation method was developed to calculate the vacuum expectation value of the stress tensor for a massive scalar field in an arbitrary gravitational field.
Abstract: A method known as covariant geodesic point separation is developed to calculate the vacuum expectation value of the stress tensor for a massive scalar field in an arbitrary gravitational field. The vacuum expectation value will diverge because the stress-tensor operator is constructed from products of field operators evaluated at the same space-time point. To remedy this problem, one of the field operators is taken to a nearby point. The resultant vacuum expectation value is finite and may be expressed in terms of the Hadamard elementary function. This function is calculated using a curved-space generalization of Schwinger's proper-time method for calculating the Feynman Green's function. The expression for the Hadamard function is written in terms of the biscalar of geodetic interval which gives a measure of the square of the geodesic distance between the separated points. Next, using a covariant expansion in terms of the tangent to the geodesic, the stress tensor may be expanded in powers of the length of the geodesic. Covariant expressions for each divergent term and for certain terms in the finite portion of the vacuum expectation value of the stress tensor are found. The properties, uses, and limitations of the results are discussed.
445 citations
TL;DR: In this paper, the problem of quantizing scalar fields propagating in anti-de Sitter space-time is considered and a consistent quantization scheme can be devised by carefully controlling information entering and leaving the space time through its timelike spatial infinity.
Abstract: We consider the problem of quantizing scalar fields propagating in anti-de Sitter space-time. This space-time is static but not globally hyperbolic and hence the usual quantization procedures are inapplicable. Nevertheless, we show that a consistent quantization scheme can be devised by carefully controlling information entering and leaving the space-time through its timelike spatial infinity.
413 citations
TL;DR: In this paper, the polarization of the vacuum induced by gravitation is studied for massless fields in the region exterior to the horizon of a Schwarzschild black hole and the form of the renormalized expectation value of the stress tensor near the horizon and at infinity is discussed for each of these three states.
Abstract: The polarization of the vacuum induced by gravitation is studied for massless fields in the region exterior to the horizon of a Schwarzschild black hole. The renormalized value of $〈{\ensuremath{\varphi}}^{2}(x)〉$ is calculated according to the "covariant point-separation scheme" for each of the Boulware, Hartle-Hawking, and Unruh "vacua." The form of the renormalized expectation value of the stress tensor near the horizon and at infinity is discussed for each of these three states. It is found that the Unruh vacuum best approximates the state that would obtain following the gravitational collapse of a massive body in the sense that the expectation values of physical observables are finite, in a freely falling frame, on the future horizon and that this state is empty near infinity apart from an outgoing flux of a blackbody radiation. The response of an Unruh box is examined further in the light of the results obtained for the stress tensor. Finally it is shown by explicit solution of the linearized Einstein equations that the area of the horizon decreases at the rate expected from the flux at infinity.
351 citations