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

Rindler-AdS/CFT

In anti-de Sitter space a highly accelerating observer perceives a Rindler horizon. The two Rindler wedges in AdS_{d+1} are holographically dual to an entangled conformal field theory that lives on two boundaries with geometry R x H_{d-1}. For AdS_3, the holographic duality is especially tractable, allowing quantum-gravitational aspects of Rindler horizons to be probed. We recover the thermodynamics of Rindler-AdS space directly from the boundary conformal field theory. We derive the temperature from the two-point function and obtain the Rindler entropy density precisely, including numerical factors, using the Cardy formula. We also probe the causal structure of the spacetime, and find from the behavior of the one-point function that the CFT "knows" when a source has fallen across the Rindler horizon. This is so even though, from the bulk point of view, there are no local signifiers of the presence of the horizon. Finally, we discuss an alternate foliation of Rindler-AdS which is dual to a CFT living in de Sitter space.Comment: 29 Pages, 4 Figures, citations adde

Enhanced Instability of de Sitter Space in Einstein-Gauss-Bonnet Gravity

We show that the addition of a topological Gauss-Bonnet term to the gravitational action can greatly increase the instability of four-dimensional de Sitter space, by favoring the nucleation of black holes. The pair-production rate given by the Euclidean action for the instanton takes the form exp(Delta S) where S is the entropy in Einstein-Gauss-Bonnet theory. The coefficient of the Gauss-Bonnet term in the action sets a stability bound on the curvature of empty de Sitter space. For that coefficient in the low-energy effective action of heterotic string theory, the maximal curvature of de Sitter space is in general much lower than the Planck scale.Comment: 8 page

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

Rotating Rindler-AdS Space

If the Hamiltonian of a quantum field theory is taken to be a timelike isometry, the vacuum state remains empty for all time. We search for such stationary vacua in anti-de Sitter space. By considering conjugacy classes of the Lorentz group, we find interesting one-parameter families of stationary vacua in three-dimensional anti-de Sitter space. In particular, there exists a family of rotating Rindler vacua, labeled by the rotation parameter beta, which are related to the usual Rindler vacuum by non-trivial Bogolubov transformations. Rotating Rindler-AdS space possesses not only an observer-dependent event horizon but even an observer-dependent ergosphere. We also find rotating vacua in global AdS provided a certain region of spacetime is excluded.Comment: 14 pages, LaTe

The Noise of Gravitons

We show that when the gravitational field is treated quantum-mechanically, it induces fluctuations -- noise -- in the lengths of the arms of gravitational wave detectors. The characteristics of the noise depend on the quantum state of the gravitational field, and can be calculated exactly in several interesting cases. For coherent states the noise is very small, but it can be greatly enhanced in thermal and (especially) squeezed states. Detection of this fundamental noise would constitute direct evidence for the quantization of gravity and the existence of gravitons.Comment: First prize in the Gravity Research Foundation Essay Competition. 6 page