Quantisation of Conformal Fields in Three-dimensional Anti-de Sitter Black Hole Spacetime

Utilizing the conformal-flatness nature of 3-dim. Anti-de Sitter (AdS_3) black hole solution of Banados, Teitelboim and Zanelli, the quantisation of conformally-coupled scalar and spinor fields in this background spacetime is explicitly carried out. In particular, mode expansion forms and propagators of the fields are obtained in closed forms. The vacuum in this conformally-coupled field theories in AdS_3 black hole spacetime, which is conformally-flat, is the conformal vacuum which is unique and has global meaning. This point particularly suggests that now the particle production by AdS_3 black hole spacetime should be absent. General argument establishing the absence of real particle creation by AdS_3 black hole spacetime for this case of conformal triviality is provided. Then next, using the explicit mode expansion forms for conformally-coupled scalar and spinor fields, the bosonic and fermionic superradiances are examined and found to be absent confirming the expectation.Comment: 51 pages, Revtex, version to appear in Int. J. Mod. Phys.

Back-reaction of a conformal field on a three-dimensional black hole

The first order corrections to the geometry of the (2+1)-dimensional black hole due to back-reaction of a massless conformal scalar field are computed. The renormalized stress energy tensor used as the source of Einstein equations is computed with the Green function for the black-hole background with transparent boundary conditions. This tensor has the same functional form as the one found in the nonperturbative case which can be exactly solved. Thus, a static, circularly symmetric and asymptotically anti-de Sitter black hole solution of the semiclassical equations is found. The corrections to the thermodynamic quantities are also computed.Comment: 12 pages, RevTeX, no figure

Scalar field quantization on the 2+1 dimensional black hole background

The quantization of a massless conformally coupled scalar field on the 2+1 dimensional Anti de Sitter black hole background is presented. The Green's function is calculated, using the fact that the black hole is Anti de Sitter space with points identified, and taking into account the fact that the black hole spacetime is not globally hyperbolic. It is shown that the Green's function calculated in this way is the Hartle-Hawking Green's function. The Green's function is used to compute $\langle T^\mu_\nu \rangle$, which is regular on the black hole horizon, and diverges at the singularity. A particle detector response function outside the horizon is also calculated and shown to be a fermi type distribution. The back-reaction from $\langle T_{\mu\nu} \rangle$ is calculated exactly and is shown to give rise to a curvature singularity at $r=0$ and to shift the horizon outwards. For $M=0$ a horizon develops, shielding the singularity. Some speculations about the endpoint of evaporation are discussed.Comment: CTP 2243, 24 pages, RevTex. (The backreaction section is extended, and some confusing notation has been changed

Non-Extreme and Ultra-Extreme Domain Walls and Their Global Space-Times

Non-extreme walls (bubbles with two insides) and ultra-extreme walls (bubbles of false vacuum decay) are discussed. Their respective energy densities are higher and lower than that of the corresponding extreme (supersymmetric), planar domain wall. These singularity free space-times exhibit non-trivial causal structure analogous to certain non-extreme black holes. We focus on anti-de~Sitter--Minkowski walls and comment on Minkowski--Minkowski walls with trivial extreme limit, as well as walls adjacent to de~Sitter space-times with no extreme limit.Comment: Revised version, 4 pages of REVTEX, UPR-546-T/Rev. Two figures not included. This version contains further elaboration of the space-time causal structur

Entropy of scalar fields in 3+1 dimensional constant curvature black hole background

We consider the thermodynamics of minimally coupled massive scalar field in 3+1 dimensional constant curvature black hole background. The brick wall model of 't Hooft is used. When Scharzschild like coordinates are used it is found that apart from the usual radial brick wall cut-off parammeter an angular cut-off parameter is required to regularize the solution. Free energy of the scalar field is obtained through counting of states using the WKB approximation. It is found that the free energy and the entropy are logarithmically divergent in both the cut-off parameters.Comment: 9 pages, LaTe

Thick domain wall universes

We investigate the spacetime of a thick gravitating domain wall for a general potential $V(\Phi)$. Using general analytical arguments we show that all nontrivial solutions fall into two categories: those interpretable as an isolated domain wall with a cosmological event horizon, and those which are pure false vacuum de Sitter solutions. Although this latter solution is always unstable to the field rolling coherently to its true vacuum, we show that there is an additional instability to wall formation if the scalar field does not couple too strongly to gravity. Using the $\lambda \Phi^4$ and sine-Gordon models as illustrative examples, we investigate the phase space of the gravitating domain wall in detail numerically, following the solutions from weak to strong gravity. We find excellent agreement with the analytic work. Then, we analyse the domain wall in the presence of a cosmological constant finding again the two kinds of solutions, wall and de Sitter, even in the presence of a negative cosmological constant.Comment: 20 pages revtex, epsfig, references added, some conclusions altere

Quantum Properties of Topological Black Holes

We examine quantum properties of topological black holes which are asymptotically anti--de Sitter. First, massless scalar fields and Weyl spinors which propagate in the background of an anti--de Sitter black hole are considered in an exactly soluble two--dimensional toy model. The Boulware--, Unruh--, and Hartle--Hawking vacua are defined. The latter results to coincide with the Unruh vacuum due to the boundary conditions necessary in asymptotically adS spacetimes. We show that the Hartle--Hawking vacuum represents a thermal equilibrium state with the temperature found in the Euclidean formulation. The renormalized stress tensor for this quantum state is well--defined everywhere, for any genus and for all solutions which do not have an inner Cauchy horizon, whereas in this last case it diverges on the inner horizon. The four--dimensional case is finally considered, the equilibrium states are discussed and a luminosity formula for the black hole of any genus is obtained. Since spacelike infinity in anti--de Sitter space acts like a mirror, it is pointed out how this would imply information loss in gravitational collapse. The black hole's mass spectrum according to Bekenstein's view is discussed and compared to that provided by string theory.Comment: 31 pages, one additional figure, enlarged discussion of the higher genus case, comment on the mass and new references adde

Brick Walls and AdS/CFT

We discuss the relationship between the bulk-boundary correspondence in Rehren's algebraic holography (and in other 'fixed-background' approaches to holography) and in mainstream 'Maldacena AdS/CFT'. Especially, we contrast the understanding of black-hole entropy from the viewpoint of QFT in curved spacetime -- in the framework of 't Hooft's 'brick wall' model -- with the understanding based on Maldacena AdS/CFT. We show that the brick-wall modification of a Klein Gordon field in the Hartle-Hawking-Israel state on 1+2-Schwarzschild AdS (BTZ) has a well-defined boundary limit with the same temperature and entropy as the brick-wall-modified bulk theory. One of our main purposes is to point out a close connection, for general AdS/CFT situations, between the puzzle raised by Arnsdorf and Smolin regarding the relationship between Rehren's algebraic holography and mainstream AdS/CFT and the puzzle embodied in the 'correspondence principle' proposed by Mukohyama and Israel in their work on the brick-wall approach to black hole entropy. Working on the assumption that similar results will hold for bulk QFT other than the Klein Gordon field and for Schwarzschild AdS in other dimensions, and recalling the first author's proposed resolution to the Mukohyama-Israel puzzle based on his 'matter-gravity entanglement hypothesis', we argue that, in Maldacena AdS/CFT, the algebra of the boundary CFT is isomorphic only to a proper subalgebra of the bulk algebra, albeit (at non-zero temperature) the (GNS) Hilbert spaces of bulk and boundary theories are still the 'same' -- the total bulk state being pure, while the boundary state is mixed (thermal). We also argue from the finiteness of its boundary (and hence, on our assumptions, also bulk) entropy at finite temperature, that the Rehren dual of the Maldacena boundary CFT cannot itself be a QFT and must, instead, presumably be something like a string theory.Comment: 54 pages, 3 figures. Arguments strengthened in the light of B.S. Kay `Instability of Enclosed Horizons' arXiv:1310.739

Thermodynamics and Evaporation of the 2+1-D Black Hole

The properties of canonical and microcanonical ensembles of a black hole with thermal radiation and the problem of black hole evaporation in 3-D are studied. In 3-D Einstein-anti-de Sitter gravity we have two relevant mass scales, $m_c=1/G$, and $m_p=(\hbar^2\Lambda/G)^{1/3}$, which are particularly relevant for the evaporation problem. It is argued that in the `weak coupling' regime $\Lambda<(\hbar G)^{-2}$, the end point of an evaporating black hole formed with an initial mass $m_0>m_p$, is likely to be a stable remnant in equilibrium with thermal radiation. The relevance of these results for the information problem and for the issue of back reaction is discussed. In the `strong coupling' regime, $\Lambda>(\hbar G)^{-2}$ a full fledged quantum gravity treatment is required. Since the total energy of thermal states in anti-de Sitter space with reflective boundary conditions at spatial infinity is bounded and conserved, the canonical and microcanonical ensembles are well defined. For a given temperature or energy black hole states are locally stable. In the weak coupling regime black hole states are more probable then pure radiation states.Comment: 11 pages, TAUP 2141/94, Late

Stability of degenerate Cauchy horizons in black hole spacetimes

In the multihorizon black hole spacetimes, it is possible that there are degenerate Cauchy horizons with vanishing surface gravities. We investigate the stability of the degenerate Cauchy horizon in black hole spacetimes. Despite the asymptotic behavior of spacetimes (flat, anti-de Sitter, or de Sitter), we find that the Cauchy horizon is stable against the classical perturbations, but unstable quantum mechanically.Comment: Revtex, 4 pages, no figures, references adde