Louis Witten

Some models of anisotropic spheres in general relativity

A heuristic procedure is developed to obtain interior solutions of Einstein’s equations for anisotropic matter from known solutions for isotropic matter. Five known solutions are generalized to give solutions with anisotropic sources.

Large Radius Expansion of Superstring Compactifications

We verify by an explicit perturbative calculation arguments presented recently concerning the existence of compactified solutions of superstring theory in which the spin connection is not embedded in the gauge group in the standard way but the gauge connection is a connection on a more general holomorphic vector bundle over a manifold of SU(3) holonomy.

Mass quantization of the Schwarzschild black hole

We examine the Wheeler-DeWitt equation for a static, eternal Schwarzschild black hole in Kucha{hacek r}-Brown variables and obtain its energy eigenstates. Consistent solutions vanish in the exterior of the Kruskal manifold and are nonvanishing only in the interior. The system is reminiscent of a particle in a box. States of definite parity avoid the singular geometry by vanishing at the origin. These definite parity states admit a discrete energy spectrum, depending on one quantum number which determines the Arnowitt-Deser-Misner mass of the black hole according to a relation conjectured long ago by Bekenstein M{approximately}{radical} (n) M{sub p}. If attention is restricted only to these quantized energy states, a black hole is described not only by its mass but also by its parity. States of indefinite parity do not admit a quantized mass spectrum. {copyright} {ital 1999} {ital The American Physical Society}

Toward a midisuperspace quantization of LeMaitre-Tolman-Bondi collapse models

LeMaitre-Tolman-Bondi models of spherical dust collapse have been used and continue to be used extensively to study various stellar collapse scenarios. It is by now well known that these models lead to the formation of black holes and naked singularities from regular initial data. The final outcome of the collapse, particularly in the event of naked singularity formation, depends very heavily on quantum effects during the final stages. These quantum effects cannot generally be treated semiclassically as quantum fluctuations of the gravitational field are expected to dominate before the final state is reached. We present a canonical reduction of LeMaitre-Tolman-Bondi space-times describing the marginally bound collapse of inhomogeneous dust, in which the physical radius R, the proper time of the collapsing dust {tau}, and the mass function F are the canonical coordinates R(r), {tau}(r) and F(r) on the phase space. Diracs constraint quantization leads to a simple functional (Wheeler-DeWitt) equation. The equation is solved and the solution can be employed to study some of the effects of quantum gravity during gravitational collapse with different initial conditions.

Wilson loop observables in (2 + 1)-dimensional Chern-Simons supergravity

(2 + 1)-dimensional gravity and supergravity, without a cosmological constant, can be described as Chern-Simons gauge theories of the Poincare and super-Poincare groups respectively. The only gauge invariant observables are Wilson loops.In this paper, we consider N = 2 Poincare supergravity on R × Σ, where R is “time” and the spatial hypersurface Σ is the plane with an arbitrary number, N, of isolated sources or punctures carrying super-Poincare charges, and examine Wilson loops enclosing one or more of them. We describe how to compute the Wilson loop observables and give explicit expressions for the cases of one and two sources. We also discuss the Poisson brackets between two Wilson loops and derive a rule by which they might be obtained.

Spherical gravitational collapse: Tangential pressure and related equations of state

We derive an equation for the acceleration of a fluid element in the spherical gravitational collapse of a bounded compact object made up of an imperfect fluid. We show that non-singular as well as singular solutions arise in the collapse of a fluid initially at rest and having only a tangential pressure. We obtain an exact solution of the Einstein equations, in the form of an infinite series, for collapse under tangential pressure with a linear equation of state. We show that if a singularity forms in the tangential pressure model, the conditions for the singularity to be naked are exactly the same as in the model of dust collapse.

On a static axisymmetric solution of the Einstein equations

Abstract A family of static, axisymmetric, asymptotically flat solutions of the Einstein equations is discussed. A source with an exterior described by a member of this family initially could have an area smaller than that of a n appropriately defined Schwarzchild surface. Intuition does not suggest the fate of the collapsing source.

SOME PROPERTIES OF CYLINDRICALLY SYMMETRIC EINSTEIN--MAXWELL FIELDS.

Some properties of static cylindrically symmetric universes consisting of gravitational and electromagnetic fields with a central axial mass, charge, or current density are discussed. Of three permissible distinct configurations, general solutions of the appropriate equations are given for two. The properties of the solutions of these two are then examined in greater detail. The equations of motion of test particles (both charged and uncharged) are described for some simple trajectories. The qualitative effect of the magnetic field on uncharged test particle behavior in some instances is noted as well as the qualitative distinction in the behavior of charged and uncharged test particles. The algebraically independent invariants of the Riemann tensor are calculated. A stability analysis is carried out for the two solutions when the system is subjected to radial perturbations. It turns out that both solutions are stable. The stability analysis is carried out by using the equations of the already unified fie...

An interior solution for the gamma metric

Interior solutions for a static, axially symmetric family of solutions of Einsteins equations are described. The interior solutions correspond to spatially bound matter and are properly matched to an exterior vacuum solution. The family of solutions discussed include the Schwarzschild solution as a special case. A general method is exhibited for transforming any spherically symmetric interior solution to an interior for the other members of the family of solutions. The energy density remains positive for at least a finite range of the parameter that describes the family of solutions. Two solutions are explicitly exhibited. One is transformed from the constant density Schwarzschild interior solution and one from the Adler interior solution. The first solution would be expected to be unstable under adiabatic perturbations of the matter, the second would be expected to be stable.

Quantum black holes from quantum collapse

The Schwarzschild black hole can be viewed as a special case of the marginally bound Lemaitre-Tolman- Bondi models of dust collapse which corresponds to a constant mass function. We presented a midisuperspace quantization of this model for an arbitrary mass function in a separate publication. In this article we show that our solution leads both to Bekensteins area spectrum for black holes as well as to the black hole entropy, which, in this context, is naturally interpreted as the loss of information of the original matter distribution within the collapsing dust cloud.