Energy Conservation and Hawking Radiation

The conservation of energy implies that an isolated radiating black hole cannot have an emission spectrum that is precisely thermal. Moreover, the no-hair theorem is only approximately applicable. We consider the implications for the black hole information puzzle.Comment: 6 pages, LaTex; v2: references adde

The Volume of Black Holes

We propose a definition of volume for stationary spacetimes. The proposed volume is independent of the choice of stationary time-slicing, and applies even though the Killing vector may not be globally timelike. Moreover, it is constant in time, as well as simple: the volume of a spherical black hole in four dimensions turns out to be just ${4 \over 3} \pi r_+^3$. We then consider whether it is possible to construct spacetimes that have finite horizon area but infinite volume, by sending the radius to infinity while making discrete identifications to preserve the horizon area. We show that, in three or four dimensions, no such solutions exist that are not inconsistent in some way. We discuss the implications for the interpretation of the Bekenstein-Hawking entropy.Comment: 8 pages, revte

De Sitter Space With Finitely Many States: A Toy Story

The finite entropy of de Sitter space suggests that in a theory of quantum gravity there are only finitely many states. It has been argued that in this case there is no action of the de Sitter group consistent with unitarity. In this note we propose a way out of this if we give up the requirement of having a hermitian Hamiltonian. We argue that some of the generators of the de Sitter group act in a novel way, namely by mixing in- and out-states. In this way it is possible to have a unitary S-matrix that is finite-dimensional and, moreover, de Sitter-invariant. Using Dirac spinors, we construct a simple toy model that exhibits these features.Comment: 6 pages, LaTe

New Coordinates for de Sitter Space and de Sitter Radiation

We introduce a simple coordinate system covering half of de Sitter space. The new coordinates have several attractive properties: the time direction is a Killing vector, the metric is smooth at the horizon, and constant-time slices are just flat Euclidean space. We demonstrate the usefulness of the coordinates by calculating the rate at which particles tunnel across the horizon. When self-gravitation is taken into account, the resulting tunneling rate is only approximately thermal. The effective temperature decreases through the emission of radiation.Comment: LaTeX, 10 pages; v2. references added; v3. minor sign errors fixed, reference added, journal versio

Smooth Initial Conditions from Weak Gravity

CMB measurements reveal an unnaturally smooth early universe. We propose a mechanism to make this smoothness natural by weakening the strength of gravity at early times, and therefore altering which initial conditions have low entropy.Comment: 14 pages, 5 figures. Minor changes, version appearing in PL

Holography and Rotating AdS Black Holes

We probe the AdS/CFT correspondence by comparing the thermodynamics of a rotating black hole in five-dimensional anti-de Sitter space with that of a conformal field theory on $S^3$, whose parameters come from the boundary of spacetime. In the high temperature limit, we find agreement between gauge theory and gravity in all thermodynamic quantities upto the same factor of 4/3 that appears for nonrotating holes.Comment: LaTeX, 13 pages, typos corrected, references adde

Confinement and the AdS/CFT Correspondence

We study the thermodynamics of the confined and unconfined phases of superconformal Yang-Mills in finite volume and at large N using the AdS/CFT correspondence. We discuss the necessary conditions for a smooth phase crossover and obtain an N-dependent curve for the phase boundary.Comment: 12 pages, 1 figure, RevTe