Werner Israel

University of Victoria | UVIC · Department of Physics and Astronomy

The firewall was introduced into black hole evaporation scenarios as a hypothetical device designed to break entanglements and preserve unitarity (Almheiri et.al., 2013). Here we show that the firewall actually exists and does break entanglements, but only in the context of a virtual reality for observers stationed near the horizon, who are followi...

The current scenario of black hole evaporation holds that the Hawking energy flux $F$ is powered by pair creation at the horizon. However, pair creation produces entanglements, some of which must necessarily be broken before the black hole evaporates completely. That leads to loss of information and violation of unitarity. In this paper, an alterna...

Several anomalies of black hole thermodynamics are resolved if one accepts hints from semi classical theory that in regions of strong gravity the energy density of the vacuum can become substantially negative. This leads to a picture of the horizon as a hot massless shell. As viewed in the local (Boulware) ground state, the apparent horizon is the...

This is an informal review of progress in gravitational physics and cosmological theory during the past decade and a half, and of challenges currently facing the theory.

Determining the inner structure of a black hole is really an evolutionary problem, with precisely known initial data. The evolution can in principle be followed to within Planck distances of the singularity at the inner horizon, using only well-established physical laws. This article is a progress report and a review of open questions.

The introductory section offers brief comments on recent progress towards the formulation of a cosmic censorship principle, the discovery that black holes can have non-Abelian hair, and other selected developments. The main body of the review focusses in more detail on two major topics: the precise formulation and proof of the third law of black h...

We summarize, simplify and extend recent work showing that small deviations from exact thermality in Hawking radiation, first uncovered by Kraus and Wilczek, have the capacity to carry off the maximum information content of a black hole. This goes a considerable way toward resolving a long-standing "information-loss paradox".

List of contributors; Preface; 1. An introductory survey S. W. Hawking and W. Israel; 2. The confrontation between gravitation theory and experiment C. M. Will; 3. Gravitational-radiation experiments D. H. Douglass and V. B. Braginsky; 4. The initial value problem and the dynamical formulation of general relativity A. E. Fischer and J. E. Marsden;...

It is an honour to be participating in these centenary celebrations for E. C.G Stueckelberg, one of the authentic geniuses of 20th century physics, whose visionary contributions to quantum electrodynamics, S-matrix theory and the renormalization group are still insufficiently appreciated.1

This chapter reviews the conceptual developments on black hole thermodynamics and the attempts to determine the origin of black hole entropy in terms of their horizon area. The brick wall model and an operational approach are discussed. An attempt to understand at the microlevel how the quantum black hole acquires its thermal properties is included...

These lectures are intended as a pedagogical introduction to the covariant formulation of nonequilibrium and statistical thermodynamics and kinetic theory. The various formulations of nonequilibrium thermodynamics and their individual difficulties — with causality, stability, shock structure — are critically reviewed. As an illustration of the gene...

The evaporation of a black hole formed by the collapse of matter is a nonunitary process involving loss of information. At least, this is how it appears in Hawking's semiclassical description, in which gravity is not quantized and the emergent radiation appears thermal. Since unitarity is one of the pillars of quantum mechanics there has been an un...

The metric ansatz is used to describe the gravitational field of a beam-pulse of spinning radiation (gyraton) in an arbitrary number of spacetime dimensions D. First we demonstrate that this metric belongs to the class of metrics for which all scalar invariants constructed from the curvature and its covariant derivatives vanish. Next, it is shown t...

The time evolution of a wormhole in a Friedmann universe approaching the Big Rip is studied. The wormhole is modeled by a thin spherical shell accreting the superquintessence fluid - two different models are presented. Contrary to recent claims that the wormhole overtakes the expansion of the universe and engulfs it before the Big Rip is reached, i...

This paper gives a new, simple and concise derivation of brane actions and brane dynamics in general relativity and in Einstein-Gauss-Bonnet gravity. We present a unified treatment, applicable to timelike surface layers and spacelike transition layers, and including consideration of the more difficult lightlike case. Comment: 15 pages, to appear in...

Was Einstein wrong? This paper provides a detailed technical review of Einstein's special and general relativity from an astrophysical perspective, including the historical development of the theories, experimental tests, modern applications to black holes, cosmology and parallel universes, and last but not least, novel ways of expressing their sev...

Gravitational collapse to a black hole leaves a decaying wake of gravitational waves. Some of those waves are absorbed into the hole and have dramatic effects on the geometry near the inner (Cauchy) horizon because of a diverging blueshift. Determining the inner structure of the hole is really an evolutionary problem with precisely known initial da...

Quantum effects at high accelerations and in strong gravitational fields give rise to counter-intuitive effects, such as "acceleration radiation", and mysterious connections, such as the relation between black hole area and entropy. Idealized experiments, using accelerated mirrors, descending boxes and massive shells, can help to provide intuitive...

We consider the application of the Aichelburg-Sexl boost to plane and line distributions of matter. Our analysis shows that for a domain wall the space-time after the boost is flat except on a null hypersurface which is the history of a null shell. For a cosmic string we study the influence of the boost on the conical singularity and give the new v...

We consider a quantized scalar field in a two-dimensional Minkowski spacetime with a moving mirror and propose a definition of moving-mirror entropy associated with temporarily inaccessible information about the future.

We consider a quantized scalar field in a two-dimensional Minkowski spacetime with a moving mirror and propose a definition of moving-mirror entropy associated with temporarily inaccessible information about the future.

This Essay is one of a series of invited contributions which will appear in the PASP throughout the year 2000 to mark the upcoming millennium. (Eds.)

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

The authors extend to the case where no symmetries are present the Dray-'t Hooft-Redmount relation, expressing conservation of energy in the collision of two light-like thin shells. This relation is applied to a schematic model for the internal physics of a rotating black hole. They show that Hawking's quasi-local mass increases without limit near...

Explores different possibilities for the nuclear structure of a black hole formed by a collapse with zero angular momentum. If the stress induced by vacuum polarisation along the axes of the 3-cylinders r=constant is a tension rather than a pressure, the spacetime geometry could be self-regulatory and describable semiclassically down to radii of a...

The timelike Killing vector xi of any static spacetime defines a set of equipotentials on which mod xi mod =constant. The principle that flat spacetimes have zero energy allows a unique expression for the energy, E, within any equipotential. The energy, E, is the energy of the shell of stressed matter on the equipotential that gives the same extern...

Outside it is a warm May evening, as two friends sit deep in discussion in a coffee house in Berne. "Besso, you must help me, I think I am going mad. How is it even thinkable that a light ray could overtake two reference systems with exactly the same speed if one is moving, the other at rest? Yet, if the symmetries we observe in electromagnetic phe...

The brick-wall model seeks to explain the Bekenstein-Hawking entropy as a wall-contribution to the thermal energy of ambient quantum fields raised to the Hawking temperature. Reservations have been expressed concerning the self-consistency of this model. For example, it predicts large thermal energy densities near the wall, producing a substantial...

John Wheeler has described the issue of gravitational collapse as “the greatest crisis in physics of all time”. Coming to terms with the limitless crushability of matter and the exposure of solidity as a hollow facade has also been psychologically traumatic. Acceptance and understanding of superdense objects were long impeded by blind spots and emo...

Determining the internal structure of a black hole is really an evolutionary problem, with precisely known initial data. In principle, the evolution can be followed to within Planck times of the singularity at the inner horizon, using only well-established physical laws. This article is a progress report and a survey of open questions.

Quasi-spherical light cones are lightlike hypersurfaces of the Kerr geometry that are asymptotic to Minkowski light cones at infinity. We develop 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...

In this paper we calculate the entropy of a thin spherical shell that contracts reversibly from infinity down to its event horizon. We find that, for a broad class of equations of state, the entropy of a non-extremal shell is one-quarter of its area in the black hole limit. The considerations in this paper suggest the following operational definiti...

In the 1970’s, a series of mathematical theorems established that astrophysical black holes are surprisingly simple, “hairless” objects. It appeared that their external geometries are fully characterized by no more than three parameters: mass, electric charge and angular momentum. In contrast to the quiescent exterior, the interior of the hole is h...

A general analysis of the gravitational dynamics of a medium with a continuous distribution of vorticity indicates that the answer to the question raised in the title is affirmative, contrary to a recent claim. Comment: 11 pages, LaTeX with amslatex macros

This is an introduction to the basics of a (2 + 2)-imbedding formalism, adapted to a double foliation of spacetime by a net of two intersecting families of lightlike hypersurfaces. It yields a simple and geometrically transparent decomposition of the Einstein equations, and has a variety of applications, e.g., to the characteristic initial-value pr...

We construct a static axisymmetric wormhole from the gravitational field of two Schwarzschild particles which are kept in equilibrium by strings (ropes) extending to infinity. The wormhole is obtained by matching two three-dimensional timelike surfaces surrounding each of the particles, and thus spacetime becomes nonsimply connected. Although the m...

Quantum corrections are studied for a charged black hole in a two-dimensional model obtained by spherisymmetric reduction of the 4D Einstein-Maxwell theory. The classical (tree-level) thermodynamics is re-formulated in the framework of the off-shell approach, considering systems at arbitrary temperature. This implies a conical singularity at the ho...

Two revolutionary concepts of the twentieth century—continental drift and the existence of superdense stars and black holes—had extended histories which ran in curious parallel for five decades. Between the wars each encountered a fierce and emotionally charged resistance which may have had a common psychological root. Each threatened man's instinc...

Surely there is nothing which more plainly invites ridicule than the study of black hole interiors. No matter what happens inside the hole, we can never observe it, nor will it affect anything we can observe. Penrose’s famous 1965 theorem assures the presence of a (classical) singularity internally, signalling a breakdown of all the laws of physics...

In 1930 the late Subrahmanyan Chandrasekhar showed that the pressure due to the quantum degeneracy of electrons could not support a cold star with a mass of more than about 1.4 times that of the Sun. This was the first indication that not all stars end their lives peacefully as white dwarfs – objects that slowly contract under their own gravity to...

The paper develops a $(2+2)$-imbedding formalism adapted to a double foliation of spacetime by a net of two intersecting families of lightlike hypersurfaces. 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...

We analyze the relativistic dynamical properties of Keplerian and non-Keplerian circular orbits in a general axisymmetric and stationary gravitational field, and discuss the implications for the stability of co- and counter-rotating accretion disks and tori surrounding a spinning black hole. Close to the horizon there are orbital peculiarities whic...

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. Comment: 5 pages, Latex 5 pages 2 postscript figures,Alberta-Thy-9-94

The following topics were dealt with: neutrino astrophysics; nucleosynthesis; cosmology; magnetic monopoles; dark matter; black holes; neutrino oscillations; beta decay; alpha decay; stellar internal processes; DIS; electroweak measurements.

The internal structure of a charged spherical black hole is still a topic of debate. In a nonrotating 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 cros...

Aspherical collapse to a black hole leaves in its aftermath a decaying tail of gravitational waves. These waves are strongly blueshifted and amplified near the inner horizon, and have drastic effects on the internal geometry of the hole. This introductory article surveys first attempts to understand the nature of these effects.

The Weyl curvature inside a black hole formed in a generic collapse grows, classically without bound, near to the inner horizon, due to partial absorption and blueshifting of the radiative tail of the collapse. Using a spherical model, we examine how this growth is modified by quantum effects of conformally coupled massless fields. Comment: 13 page...

Intelligent life could not have evolved in our Universe if fundamental physical parameters like the fine-structure constant had differed appreciably from their observed values. Can this peculiar coincidence be understood in terms of some evolutionary mechanism? According to Lee Smolin of Syracuse University, US (Class. Quantum Gravity (1992)9 173),...

Nonspherical collapse to a black hole leaves a decaying wake of gravitational waves. Part of this radiation is absorbed and accumulates at the black hole's inner horizon, a pathological surface marked by infinite blueshift. The blueshifted radiation has drastic effects on the geometry near and within the inner horizon. This article surveys the firs...

Ori has recently shown that an astronaut approaching the inner horizon of a black hole is not necessarily torn apart by tidal forces. This raises anew the possibility of astronavigation through black holes, perhaps to other universes. We re-examine this question in the light of hypotheses about probable conditions in the black hole core.

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.

This paper shows how the structure and dynamics of a thin shell traveling at the speed of light can be obtained from a simple and convenient prescription that is a straightforward extension and continuous limit of the familiar extrinsic-curvature algorithm for subluminal shells. It allows the space-time coordinates to be chosen freely and independe...

THE idea that our expanding Universe was born in a 'bounce'—the re-expansion of a previously contracting universe—is an old cosmogonical hypothesis, and continues to resurface1–5 despite being overshadowed recently by hypotheses inspired by Guth's inflationary model. Here we show how recent developments in the physics of black-hole interiors force...

The gravitational effects associated with the radiative tail produced by a gravitational collapse with rotation are investigated. It is shown that the infinite blueshift of the tail's energy density occurring at the Cauchy horizon of the resulting black hole causes a classically unbounded inflation of the effective internal gravitational-mass param...

It is argued that the internal evolution of a generic black hole leads to a “fat cigar” configuration near the inner (Cauchy) horizon, inside which curvatures are planckian. The mechanism responsible is an enormous inflation of the effective internal mass of the hole, caused by blueshift of the radiative tail of the collapse at the Cauchy horizon....

It is well known (or, at least, widely believed) that a loop of cosmic string exerts no gravitational force on a relatively stationary object placed very near the string filament, and in this sense is gravitationally massless. More remarkably, it has recently been stated that string loops must always be straight and cannot curve, at least on length...

Gravitational collapse with rotation leaves a slowly decaying radiative tail which becomes infinitely blueshifted at the inner horizon of the resulting black hole. We study the gravitational effects of this on the inner structure of the hole, using a simple spherical model. In the presence of outflow from the collapsing star, the gravitational-mass...

It is shown that a loop of idealized cosmic string deforms the background geometry in its vicinity so that its path and shape become geodesics of this background. For angular deficits smaller than pi, this deformation causes the background curvature to grow without bound near an infinitely thin string. However, the rate of growth is so weak that th...

The first part of the paper formulates general conditions (independent of a particular gauge-theoretic model) under which a cylindrical distribution of matter can be joined to a vacuum exterior with a conical geometry and exhibits the relation between angular deficit and internal structure. To bring out the relation to gravitational mass, the secon...

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The fourth annual Lake Louise Winter Institute, From Colliders to Cosmology, took place February 19 to 25, 1989, at the Chateau Lake Louise in the Canadian Rocky Mountains. The subject of the Institute was the new, and exciting, field of astro-particle physics which explores the interface between elementary particle physics and cosmology. An attemp...

Preface; 1. Newton's Principia S. W. Hawking; 2. Newtonianism and today's physics S. Weinberg; 3. Newton, quantum theory and reality R. Penrose; 4. Experiments on gravitation A. H. Cook; 5. Experimental gravitation from Newton's Principia to Einstein's general relativity C. M. Will; 6. The problem of motion in Newtonian and Einsteinian gravity T. D...

To commemorate the 300th anniversary of the publication of Isaac Newton's Philosophiae Naturalis Principia Mathematica, Stephen Hawking and Werner Israel assembled a series of unique review papers by many of the world's foremost researchers in cosmology, relativity, and particle physics. The resulting volume reflects the significant and exciting ad...

The formalism of the relativistic kinetic theory is adapted to the one-dimensional string's structure in order to describe the macroscopic properties of a system of cosmic strings. A distribution function is defined on the phase space by considering the number of intersections of the strings with a 2-dimensional space-like surface. The number curre...

It is shown that no continuous process in which the energy tensor of accreted matter remains bounded and satisfies the weak energy condition in a neighborhood of the apparent horizon can reduce the surface gravity of a black hole to zero within a finite advanced time. This gives a precise expression to the third law of black-hole mechanics.

It is shown that a trapped surface can be extended, in a locally area-preserving fashion, to a three-cylinder that is everywhere spacelike, provided it encounters no singularities in its development. Thus the interior of a regular, area-preserving, initially trapped surface is permanently sealed off from causal influence on the exterior world.

Circumstantial evidence favouring the broad conjecture that event horizons always form in gravitational collapse is summarized along with the mounting counterevidence to a more restrictive cosmic censorship principle, which would compel every singularity formed in the collapse to be enclosed within a horizon. A confinement theorem is presented, sta...

The first part of the article presents an introduction to the covariant formulations of phenomenological and statistical thermodynamics. In the second part the theory is applied to develop the relativistic form of the Landau two-fluid model and its microscopic validation in terms of Bose-Einstein condensation in second-quantized boson fields.

The third law of black hole mechanics is here established in the following form: no continuous process in which the stress-energy tensor of matter stays bounded and satisfies the weak energy condition in a neighbourhood of the apparent horizon can reduce the surface gravity of a black hole to zero within a finite advanced time.

This paper outlines the covariant (nonequilibrium) phenomenological theory of a relativistic superfluid, and analyzes its microscopic justification by studying the statistical thermodynamics of the superfluid in the case of thermal equilibrium, using a Euclidean path-integral formalism.

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 cosm...

The Hawking criterion for the stability of thermodynamical equilibrium between a Schwarzschild black hole and its own radiation is refined by the use of Page's expression for the renormalized stress-energy tensor.

This is the first in a series of papers, the overall objective of which is the formulation of a new covariant approach to nonequilibrium statistical mechanics in classical general relativity. The object here is the development of a tractable theory for self-gravitating systems. It is argued that the “state” of an N-particle system may be characteri...

We consider a detector enclosed in a screen which gives it a directional sensitivity. If this system is uniformly accelerated, it responds as if it were sitting in a time-independent, anisotropic bath of radiation. The radiation spectrum is thermal only if the detector samples all directions equally.

A new relativistic version of the Landau two-fluid model developed by Khalatnikov and Lebedev is shown to be equivalent to a previous formulation due to Dixon and Israel. Work partially supported by the Natural Sciences and Engineering Research Council of Canada.

The equations of radiative hydrodynamics, with inclusion of relaxation terms and couplings between the radiative flux, viscous stresses and the acceleration and angular velocity of the medium, are derived from the 14-moment approximation. The physical mechanism responsible for the bulk viscosity is discussed.

A relativistic extension of the Landau two-fluid model is developed. Work partially supported by the Natural Sciences and Engineering Research Council of Canada.

It is shown that the rest-frame of the Hawking radiation surrounding a rotating black hole revolves with the Bardeen angular velocity. The problem of evaluating the partition function is discussed. Permanent address: Theoretical Physics Institute, University of Alberta, Edmonton, Canada T6G 2J1. Research supported in part by the Natural Sciences an...

The spinor methods of Witten and Nester are generalized to show that a system satisfying the dominant energy condition has a positive total energy and a time-like four-momentum measured at space-like or future null infinity.

This paper will review recent progress in the covariant formulation of thermodynamics and statistical mechanics, with emphasis on two topics: (i) a consistent treatment of transient effects which avoids the paradox of an infinite speed of heat, and (ii) the thermodynamics of black holes.RésuméCette communication sera une revue des progrés accomplis...

The polarization concept is reduced to its most rudimentary kinematical form: the substitution of an equivalent set of multipole moments, referred to an arbitrarily chosen center, for the source density due to an eccentrically placed particle. From this the general relativistic dynamics of extended bodies is built up by superposition of infinitesim...