Werner Israel

300 Years of Gravitation

The invention relates to a novel filtering circuit whereby a phase detected output control signal is filtered and utilized to provide greater stability in a phase-locked loop. The filtering circuit is placed in the connecting path between a phase detector and an oscillator; the oscillator supplies output signals, having a repetition rate which depends on the instantaneous values of the filtered control signal. The filtering circuit comprises an adder which adds the phase detected control signal to a signal corresponding to the preceding filtered control signal multiplied by a constant factor which is less than unity (<1).

Thermo-field dynamics of black holes☆

It is shown that observers whose observation of particle modes is limited by a horizon see a “hot” thermal vacuum. This unifies and generalizes the results of Fulling, Gibbons, Hawking and Unruh. The close parallel with the thermo-field dynamics of Takahashi and Umezawa is delineated.

Quasi-spherical light cones of the Kerr geometry

Quasi-spherical light cones are lightlike hypersurfaces of the Kerr geometry that are asymptotic to Minkowski light cones at infinity. We derive the equations of these surfaces and examine their properties. In particular, we show that they are free of caustics for all positive values of the Kerr radial coordinate r. Useful applications include the propagation of high-frequency waves, the definition of Kruskal-like coordinates for a spinning black hole and the characteristic initial-value problem.

Covariant double-null dynamics: 2 + 2-splitting of the Einstein equations

We develop a (2 + 2)-imbedding formalism adapted to a double foliation of spacetime by a net of two intersecting families of lightlike hypersurfaces. The intersections define a set of 2-spaces with hypersurface-orthogonal lightlike normals. The formalism is two-dimensionally covariant, and leads to simple, geometrically transparent and tractable expressions for the Einstein field equations and the Einstein - Hilbert action, and it should find a variety of applications. It is applied here to elucidate the structure of the characteristic initial-value problem of general relativity.

STRUCTURE OF THE CHARGED SPHERICAL BLACK HOLE INTERIOR

The internal structure of a charged spherical black hole is still a topic of debate. In a non-rotating but aspherical gravitational collapse to form a spherical charged black hole, the backscattered gravitational wave tails enter the black hole and are blueshifted at the Cauchy horizon. This has a catastrophic effect if combined with an outflux crossing the Cauchy horizon: a singularity develops at the Cauchy horizon and the effective mass inflates. Recently, a numerical study of a massless scalar field in the Reissner-Nordström background suggested that a spacelike singularity may form before the Cauchy horizon forms. We will show that there exists an approximate analytic solution of the scalar-field equations which allows the mass-inflation singularity at the Cauchy horizon to exist. In particular, we see no evidence that the Cauchy horizon is preceded by a spacelike singularity.

Structure of the inner singularity of a spherical black hole.

We review the evidence for and against the possibility that the inner singularity of a black hole contains a lightlike segment which is locally mild and characterized by mass inflation.

Analytic models of nonspherical collapse, cosmic censorship and the hoop conjecture

Abstract Thin shells collapsing with the speed of light provide simple analytical counterparts of the models of prolate collapse to spindle singularities recently studied numerically by Shapiro and Teukolsky. For highly elongated sources these singularities are possibly naked.

The third law of black hole mechanics: What is it?

Abstract By consideration of a simple example it is demonstrated that a third “law” of black hole mechanics cannot be valid unless the energy tensor of accreting matter is bounded and satisfies a positive energy condition outside apparent horizons.

Does a cosmic censor exist

A distinction is drawn between the event horizon conjecture (EHC), the conjecture that an event horizon forms in a gravitational collapse, and cosmic censorship, the idea that every singularity which develops in the course of collapse must be enclosed within a horizon. It is argued that a body of circumstantial evidence seems to favor EHC, but cosmic censorship seems contraindicated.

Quantum flux from a moving spherical mirror

We calculate the flux from a spherical mirror which is expanding or contracting with nearly uniform acceleration. The flux at an exterior point (which could in principle be a functional of the mirrors past history) is actually found to be a local function, depending on the first and second time derivatives of acceleration at the retarded time.