Gary T. Horowitz

Higher-dimensional resolution of dilatonic black-hole singularities

We show that the four-dimensional extreme dilaton black hole with dilaton coupling constant can be interpreted as a completely non-singular, non-dilatonic, black p-brane in (4+p) dimensions provided that p is odd. Similar results are obtained for multi-black-holes and dilatonic extended objects in higher spacetime dimensions. The non-singular black p-brane solutions include the self-dual 3-brane of ten-dimensional N=2B supergravity and a multi-5-brane solution of eleven-dimensional supergravity. In the case of a supersymmetric non-dilatonic p-brane solution of a supergravity theory, we show that it saturates a bound on the energy per unit p-volume of all field configurations of appropriate asymptotic behaviour which are non-singular on some initial hypersurface.

Positive mass theorems for black holes

We extend Wittens proof of the positive mass theorem at spacelike infinity to show that the mass is positive for initial data on an asymptotically flat spatial hypersurface Σ which is regular outside an apparent horizonH. In addition, we prove that if a black hole has electromagnetic charge, then the mass is greater than the modulus of the charge. These results are also valid for the Bondi mass at null infinity. Finally, in the case of the Einstein equation with a negative cosmological constant, we show that a suitably defined mass is positive for data on an asymptotically anti-de Sitter surface Σ which is regular outside an apparent horizon.

Exact solutions and singularities in string theory

We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail.

Energy-momentum of isolated systems cannot be null

Abstract It is shown that neither the ADM nor the Bondi four-momentum of an isolated system in general relativity can be null. This strengthens recent results on positivity of energy by showing that the total four-moemtum must be strictly timelike (and future directed).

Phase space of general relativity revisited: A canonical choice of time and simplification of the Hamiltonian

The phase space of general relativity is considered in the asymptotically flat context. Using spinorial techniques introduced by Witten, a prescription is given to transport rigidly the space‐time translations at infinity to the interior of the (spatial) three‐manifold. This yields a preferred four‐parameter family of lapses and shifts and hence reduces the infinite‐dimensional freedom in the choice of ‘‘time’’ to the restricted freedom available in special relativity. The corresponding Hamiltonians are computed and are shown to have an especially simple form: the Hamiltonians are ‘‘diagonal’’ in the (spatial) derivatives of variables which define ‘‘time.’’ Furthermore, the Hamiltonians (generating timelike translations) are shown to be positive in a neighborhood of the constraint submanifold of the phase space, even at points at which the ADM energy is negative.

Black holes and the stability of gravitation

The existence of black holes in general relativity provides an effective cutoff to the negative gravitational potential. This results in a fundamental upper limit on the amount of energy that can be radiated away by any isolated system.