The Gravitational Hamiltonian in the Presence of Non-Orthogonal Boundaries

This paper generalizes earlier work on Hamiltonian boundary terms by omitting the requirement that the spacelike hypersurfaces $\Sigma_t$ intersect the timelike boundary $\cal B$ orthogonally. The expressions for the action and Hamiltonian are calculated and the required subtraction of a background contribution is discussed. The new features of a Hamiltonian formulation with non-orthogonal boundaries are then illustrated in two examples.Comment: 23 pages, 1 figure, LaTeX. The action is altered to include a corner term which results in a different value for the non-orthogonal term. An additional appendix with Euclidean results is included. To appear in Class. Quant. Gra

The Superscattering Matrix for Two Dimensional Black Holes

A consistent Euclidean semi classical calculation is given for the superscattering operator $\$$ in the RST model for states with a constant flux of energy. The $\$$ operator is CPT invariant. There is no loss of quantum coherence when the energy flux is less than a critical rate and complete loss when the energy flux is critical.Comment: 12 pages (R/94/4

Virtual Black Holes

One would expect spacetime to have a foam-like structure on the Planck scale with a very high topology. If spacetime is simply connected (which is assumed in this paper), the non-trivial homology occurs in dimension two, and spacetime can be regarded as being essentially the topological sum of $S^2\times S^2$ and $K3$ bubbles. Comparison with the instantons for pair creation of black holes shows that the $S^2\times S^2$ bubbles can be interpreted as closed loops of virtual black holes. It is shown that scattering in such topological fluctuations leads to loss of quantum coherence, or in other words, to a superscattering matrix $\$$ that does not factorise into an $S$ matrix and its adjoint. This loss of quantum coherence is very small at low energies for everything except scalar fields, leading to the prediction that we may never observe the Higgs particle. Another possible observational consequence may be that the $\theta$ angle of QCD is zero without having to invoke the problematical existence of a light axion. The picture of virtual black holes given here also suggests that macroscopic black holes will evaporate down to the Planck size and then disappear in the sea of virtual black holes.Comment: 24p, LaTeX, 3 postscript figures included with epsf sent in a seperate uuencoded fil

A note on the entropy of charged multi - black - holes

Majumdar--Papapetrou multi--black-hole solutions of the Einstein--Maxwell equations are considered in four and higher dimensions. The Euclidean action with boundary conditions appropriate to the canonical ensemble is shown to lead to zero entropy.Comment: LaTeX, 8 page

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

Quantum Coherence in Two Dimensions

The formation and evaporation of two dimensional black holes are discussed. It is shown that if the radiation in minimal scalars has positive energy, there must be a global event horizon or a naked singularity. The former would imply loss of quantum coherence while the latter would lead to an even worse breakdown of predictability. CPT invariance would suggest that there ought to be past horizons as well. A way in which this could happen with wormholes is described.Comment: 11 pages, DAMTP-R93/15, CALT-68-1861, Tex, 3 appended uuencoded figure

From 'nothing' to inflation and back again

A procedure for solving Wheeler-DeWitt equation in Euclidean region, following step by step the construction of tunneling wave function in nonrelativistic quantum mechanics by Banks, Bender and Wu, is proposed. Solutions for a universe satisfying no-boundary condition and a universe created from 'nothing' are compared to the corresponding solutions for a particle in a two-dimensional potential well, and effects of indefiniteness of metric and zero energy in Wheeler-DeWitt equation are discussed.Comment: 8 pages, presented at the conference Relativity and Gravitation, 100 years after Einstein in Prague (Prague 2012

Relationship between Hawking Radiation and Gravitational Anomalies

We show that in order to avoid a breakdown of general covariance at the quantum level the total flux in each outgoing partial wave of a quantum field in a black hole background must be equal to that of a (1+1)-dimensional blackbody at the Hawking temperature.Comment: 5 pages, 1 figure; v2: typo corrected, reference added; v3: comment added, minor editorial changes to agree with published versio

Can Extremal Black Holes Have Non-Zero Entropy ?

We give several pieces of evidence to show that extremal black holes cannot be obtained as limits of non-extremal black holes. We review arguments in the literature showing that the entropy of extremal black holes is zero, while that of near-extremal ones obey the Bekenstein-Hawking formula. However, from the counting of degeneracy of quantum (BPS) states of string theory the entropy of extremal stringy black holes obeys the area law. An attempt is made to reconcile these arguments.Comment: 18 pages, RevTEX; last section modified, version to appear in Mod. Phys. Lett.

The Semi-Classical Back Reaction to Black Hole Evaporation

The semi-classical back reaction to black hole evaporation (wherein the renormalized energy momentum tensor is taken as source of Einstein's equations) is analyzed in detail. It is proven that the mass of a Schwarzshild black hole decreases according to Hawking's law $dM/dt = - C/ M^2$ where $C$ is a constant of order one and that the particles are emitted with a thermal spectrum at temperature $1/8\pi M(t)$.Comment: 10 pages, LATE