Naked and Thunderbolt Singularities in Black Hole Evaporation

If an evaporating black hole does not settle down to a non radiating remnant, a description by a semi classical Lorentz metric must contain either a naked singularity or what we call a thunderbolt, a singularity that spreads out to infinity on a spacelike or null path. We investigate this question in the context of various two dimensional models that have been proposed. We find that if the semi classical equations have an extra symmetry that make them solvable in closed form, they seem to predict naked singularities but numerical calculations indicate that more general semi classical equations, such as the original CGHS ones give rise to thunderbolts. We therefore expect that the semi classical approximation in four dimensions will lead to thunderbolts. We interpret the prediction of thunderbolts as indicating that the semi classical approximation breaks down at the end point of black hole evaporation, and we would expect that a full quantum treatment would replace the thunderbolt with a burst of high energy particles. The energy in such a burst would be too small to account for the observed gamma ray bursts.Comment: 21 pages (10 diagrams available on request

Open Inflation With Scalar-tensor Gravity

The open inflation model recently proposed by Hawking and Turok is investigated in scalar-tensor gravity context. If the dilaton-like field has no potential, the instanton of our model is singular but has a finite action. The Gibbons-Hawking surface term vanishes and hence, can not be used to make $\Omega_0$ nonzero. To obtain a successful open inflation one should introduce other matter fields or a potential for the dilaton-like fields.Comment: 10 pages.1 figure. Some comments and references are improved. to be published in PR

Entropy in the RST Model

The RST Model is given boundary term and Z-field so that it is well-posed and local. The Euclidean method is described for general theory and used to calculate the RST intrinsic entropy. The evolution of this entropy for the shockwave solutions is found and obeys a second law.Comment: 10 pages, minor revisions, published version in Late

Decoherence, Re-coherence, and the Black Hole Information Paradox

We analyze a system consisting of an oscillator coupled to a field. With the field traced out as an environment, the oscillator loses coherence on a very short {\it decoherence timescale}; but, on a much longer {\it relaxation timescale}, predictably evolves into a unique, pure (ground) state. This example of {\it re-coherence} has interesting implications both for the interpretation of quantum theory and for the loss of information during black hole evaporation. We examine these implications by investigating the intermediate and final states of the quantum field, treated as an open system coupled to an unobserved oscillator.Comment: 23 pages, 2 figures included, figures 3.1 - 3.3 available at http://qso.lanl.gov/papers/Papers.htm

Homogeneous Modes of Cosmological Instantons

We discuss the O(4) invariant perturbation modes of cosmological instantons. These modes are spatially homogeneous in Lorentzian spacetime and thus not relevant to density perturbations. But their properties are important in establishing the meaning of the Euclidean path integral. If negative modes are present, the Euclidean path integral is not well defined, but may nevertheless be useful in an approximate description of the decay of an unstable state. When gravitational dynamics is included, counting negative modes requires a careful treatment of the conformal factor problem. We demonstrate that for an appropriate choice of coordinate on phase space, the second order Euclidean action is bounded below for normalized perturbations and has a finite number of negative modes. We prove that there is a negative mode for many gravitational instantons of the Hawking-Moss or Coleman-De Luccia type, and discuss the associated spectral flow. We also investigate Hawking-Turok constrained instantons, which occur in a generic inflationary model. Implementing the regularization and constraint proposed by Kirklin, Turok and Wiseman, we find that those instantons leading to substantial inflation do not possess negative modes. Using an alternate regularization and constraint motivated by reduction from five dimensions, we find a negative mode is present. These investigations shed new light on the suitability of Euclidean quantum gravity as a potential description of our universe.Comment: 16 pages, compressed and RevTex file, including one postscript figure fil

de Sitter geodesics: reappraising the notion of motion

The de Sitter spacetime is transitive under a combination of translations and proper conformal transformations. Its usual family of geodesics, however, does not take into account this property. As a consequence, there are points in de Sitter spacetime which cannot be joined to each other by any one of these geodesics. By taking into account the appropriate transitivity properties in the variational principle, a new family of maximizing trajectories is obtained, whose members are able to connect any two points of the de Sitter spacetime. These geodesics introduce a new notion of motion, given by a combination of translations and proper conformal transformations, which may possibly become important at very-high energies, where conformal symmetry plays a significant role.Comment: 9 pages. V2: Presentation changes aiming at clarifying the text; version accepted for publication in Gen. Rel. Gra

Geometric Entropy of Nonrelativistic Fermions and Two Dimensional Strings

We consider the geometric entropy of free nonrelativistic fermions in two dimensions and show that it is ultraviolet finite for finite fermi energies, but divergent in the infrared. In terms of the corresponding collective field theory this is a {\em nonperturbative} effect and is related to the soft behaviour of the usual thermodynamic entropy at high temperatures. We then show that thermodynamic entropy of the singlet sector of the one dimensional matrix model at high temperatures is governed by nonperturbative effects of the underlying string theory. In the high temperature limit the ``exact'' expression for the entropy is regular but leads to a negative specific heat, thus implying an instability. We speculate that in a properly defined two dimensional string theory, the thermodynamic entropy could approach a constant at high temperatures and lead to a geometric entropy which is finite in the ultraviolet.Comment: LaTex, 19 pages, no figures. Some references adde

Entropy of Lovelock Black Holes

A general formula for the entropy of stationary black holes in Lovelock gravity theories is obtained by integrating the first law of black hole mechanics, which is derived by Hamiltonian methods. The entropy is not simply one quarter of the surface area of the horizon, but also includes a sum of intrinsic curvature invariants integrated over a cross section of the horizon.Comment: 15 pages, plain Latex, NSF-ITP-93-4

Convenient Versus Unique Effective Action Formalism in 2D Dilaton-Maxwell Quantum Gravity

The structure of one-loop divergences of two-dimensional dilaton-Maxwell quantum gravity is investigated in two formalisms: one using a convenient effective action and the other a unique effective action. The one-loop divergences (including surface divergences) of the convenient effective action are calculated in three different covariant gauges: (i) De Witt, (ii) $\Omega$-degenerate De Witt, and (iii) simplest covariant. The on-shell effective action is given by surface divergences only (finiteness of the $S$-matrix), which yet depend upon the gauge condition choice. Off-shell renormalizability is discussed and classes of renormalizable dilaton and Maxwell potentials are found which coincide in the cases of convenient and unique effective actions. A detailed comparison of both situations, i.e. convenient vs. unique effective action, is given. As an extension of the procedure, the one-loop effective action in two-dimensional dilaton-Yang-Mills gravity is calculated.Comment: 25 pages, LaTeX file, HUPD-93-0

Non-extremal Stringy Black Hole

We construct a four-dimensional BPS saturated heterotic string solution from the Taub-NUT solution. It is a non-extremal black hole solution since its Euler number is non-zero. We evaluate its black hole entropy semiclassically. We discuss the relation between the black hole entropy and the degeneracy of string states. The entropy of our string solution can be understood as the microscopic entropy which counts the elementary string states without any complications.Comment: 18 pages, Late