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

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

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

Generalized entropy and Noether charge

We find an expression for the generalized gravitational entropy of Hawking in terms of Noether charge. As an example, the entropy of the Taub-Bolt spacetime is calculated.Comment: 6 pages, revtex, reference correcte

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

Conformal Invariance of Black Hole Temperature

It is shown that the surface gravity and temperature of a stationary black hole are invariant under conformal transformations of the metric that are the identity at infinity. More precisely, we find a conformal invariant definition of the surface gravity of a conformal Killing horizon that agrees with the usual definition(s) for a true Killing horizon and is proportional to the temperature as defined by Hawking radiation. This result is reconciled with the intimate relation between the trace anomaly and the Hawking effect, despite the {\it non}invariance of the trace anomaly under conformal transformations.Comment: 8 pages, plain LaTeX, NSF-ITP-93-9

Universal criterion for black hole stability

It is shown that a non-rotating macroscopic black hole with very large horizon area can remain in stable thermal equilibrium with Hawking radiation provided {\it its mass, as a function of horizon area, exceeds its microcanonical entropy, i.e., its entropy when isolated, without thermal radiation or accretion, and having a constant horizon area} (in appropriate units). The analysis does not use properties of specific classical spacetimes, but depends only on the plausible assumption that the mass is a function of the horizon area for large areas.Comment: 6 pages Latex, no figures; an equation adde

Modified Gravity with a Non-minimal Gravitational Coupling to Matter

We consider modified theories of gravity with a direct coupling between matter and geometry, denoted by an arbitrary function in terms of the Ricci scalar. Due to such a coupling, the matter stress tensor is no longer conserved and there is an energy transfer between the two components. By solving the conservation equation, we argue that the matter system should gain energy in this interaction, as demanded by the second law of thermodynamics. In a cosmological setting, we show that although this kind of interaction may account for cosmic acceleration, this latter together with direction of the energy transfer constrain the coupling function.Comment: 13 Pages, Two figures, Accepted for publication in Physical Review