Information Loss in Black Holes

The question of whether information is lost in black holes is investigated using Euclidean path integrals. The formation and evaporation of black holes is regarded as a scattering problem with all measurements being made at infinity. This seems to be well formulated only in asymptotically AdS spacetimes. The path integral over metrics with trivial topology is unitary and information preserving. On the other hand, the path integral over metrics with non-trivial topologies leads to correlation functions that decay to zero. Thus at late times only the unitary information preserving path integrals over trivial topologies will contribute. Elementary quantum gravity interactions do not lose information or quantum coherence

Closed Trapped Surfaces in Cosmology

The existence of closed trapped surfaces need not imply a cosmological singularity when the spatial hypersurfaces are compact. This is illustrated by a variety of examples, in particular de Sitter spacetime admits many closed trapped surfaces and obeys the null convergence condition but is non-singular in the k=+1 frame.Comment: 11 pages. To appear in GRG, Vol 35 (August issue

Hawking radiation in an electro-magnetic wave-guide?

It is demonstrated that the propagation of electro-magnetic waves in an appropriately designed wave-guide is (for large wave-lengths) analogous to that within a curved space-time -- such as around a black hole. As electro-magnetic radiation (e.g., micro-weaves) can be controlled, amplified, and detected (with present-day technology) much easier than sound, for example, we propose a set-up for the experimental verification of the Hawking effect. Apart from experimentally testing this striking prediction, this would facilitate the investigation of the trans-Planckian problem. PACS: 04.70.Dy, 04.80.-y, 42.50.-p, 84.40.Az.Comment: 4 pages RevTeX, 1 figur

Gravitational Entropy and Global Structure

The underlying reason for the existence of gravitational entropy is traced to the impossibility of foliating topologically non-trivial Euclidean spacetimes with a time function to give a unitary Hamiltonian evolution. In $d$ dimensions the entropy can be expressed in terms of the $d-2$ obstructions to foliation, bolts and Misner strings, by a universal formula. We illustrate with a number of examples including spaces with nut charge. In these cases, the entropy is not just a quarter the area of the bolt, as it is for black holes.Comment: 18 pages. References adde

Entropy of Rotating Misner String Spacetimes

Using a boundary counterterm prescription motivated by the AdS/CFT conjecture, I evaluate the energy, entropy and angular momentum of the class of Kerr-NUT/bolt-AdS spacetimes. As in the non-rotating case, when the NUT charge is nonzero the entropy is no longer equal to one-quarter of the area due to the presence of the Misner string. When the cosmological constant is also non-zero, the entropy is bounded from above.Comment: Revtex, 9 pages, 3 figure

Large N Phases, Gravitational Instantons and the Nuts and Bolts of AdS Holography

Recent results in the literature concerning holography indicate that the thermodynamics of quantum gravity (at least with a negative cosmological constant) can be modeled by the large N thermodynamics of quantum field theory. We emphasize that this suggests a completely unitary evolution of processes in quantum gravity, including black hole formation and decay; and even more extreme examples involving topology change. As concrete examples which show that this correspondence holds even when the space-time is only locally asymptotically AdS, we compute the thermodynamical phase structure of the AdS-Taub-NUT and AdS-Taub-Bolt spacetimes, and compare them to a 2+1 dimensional conformal field theory (at large N) compactified on a squashed three sphere, and on the twisted plane.Comment: 20 pages, three figures. (uses harvmac.tex and epsf.tex

Higher Spin Field Equation in a Virtual Black Hole Metric

In a quantum theory of gravity, fluctuations about the vacuum may be considered as Planck scale virtual black holes appearing and annihilating in pairs. Incident fields scattering from such fluctuations would lose quantum coherence. In a recent paper (hep-th/9705147), Hawking and Ross obtained an estimate for the magnitude of this loss in the case of a scalar field. Their calculation exploited the separability of the conformally invariant scalar wave equation in the electrovac C metric background, which is justified as a sufficiently good description of a virtual black hole pair in the limit considered. In anticipation of extending this result, the Teukolsky equations for incident fields of higher spin are separated on the vacuum C metric background and solved in the same limit. With the exception of spin 2 fields, these equations are shown in addition to be valid on the electrovac C metric background. The angular solutions are found to reduce to the spin- weighted spherical harmonics, and the radial solutions are found to approach hypergeometrics close to the horizons. By defining appropriate scattering boundary conditions, these solutions are then used to estimate the transmission and reflection coefficients for an incident field of spin s. The transmission coefficient is required in order to estimate the loss of quantum coherence of an incident field through scattering off virtual black holes.Comment: 23 pages, 3 figures, LaTeX, minor typo correcte

Dynamic and Thermodynamic Stability and Negative Modes in Schwarzschild-Anti-de Sitter

The thermodynamic properties of Schwarzschild-anti-de Sitter black holes confined within finite isothermal cavities are examined. In contrast to the Schwarzschild case, the infinite cavity limit may be taken which, if suitably stated, remains double valued. This allows the correspondence between non-existence of negative modes for classical solutions and local thermodynamic stability of the equilibrium configuration of such solutions to be shown in a well defined manner. This is not possible in the asymptotically flat case. Furthermore, the non-existence of negative modes for the larger black hole solution in Schwarzschild-anti-de Sitter provides strong evidence in favour of the recent positive energy conjecture by Horowitz and Myers.Comment: 21 pages, 5 figures, LaTe

Misner String Entropy

I show that gravitational entropy can be ascribed to spacetimes containing Misner strings (the gravitational analogues of Dirac strings), even in the absence of any other event horizon (or bolt) structures. This result follows from an extension of proposals for evaluating the stress-energy of a gravitational system which are motivated by the AdS/CFT correspondence.Comment: revtex, 5 pages, references added, typo correcte

Entanglement entropy of the black hole horizon

We examine a possibility that, when a black hole is formed, the information on the collapsed star is stored as the entanglement entropy between the outside and the thin region (of the order of the Planck length) of the inside the horizon. For this reason, we call this as the entanglement entropy of the black hole ``horizon''. We construct two models, one is in the Minkowski spacetime and the other is in the Rindler wedge. To calculate the entropy explicitly, we assume that the thin regions of the order of the Planck length of the outside and inside the horizon are completely entangled by quantum effects. We also use a property of the entanglement entropy that it is symmetric under an interchange of the observed and unobserved subsystems. Our setting and this symmetric property substantially reduce the needed numerical calculation. As a result of our analysis, we can explain the Bekenstein-Hawking entropy itself (rather than its correction by matter fields) in the context of the entanglement entropy.Comment: 28 pages, 5 figures, section 1 and the paragraph before subsection 3.1 are improved and enlarge