Jacob D. Bekenstein

Spectroscopy of the quantum black hole

Abstract We develop the idea that, in quantum gravity where the horizon fluctuates, a black hole should have a discrete mass spectrum with concomitant line emission. Simple arguments fix the spacing of the lines, which should be broad but unblended. Assuming uniformity of the matrix elements for quantum transitions between near levels, we work out the probabilities for the emission of a specified series of quanta and the intensities of the spectral lines. The thermal character of the radiation is entirely due to the degeneracy of the levels, the same degeneracy that becomes manifest as black hole entropy. One prediction is that there should be no lines with wavelength of the order of the black hole size or larger. This makes it possible to test quantum gravity with black holes well above Planck scale.

Exact solutions of Einstein-conformal scalar equations

The massless scalar field which satisfies a conformally invariant equation is in some respects more interesting than the ordinary one. Unfortunately, few, if any, exact solutions of Einsteins equations for a conformal scalar stress-energy have appeared previously. Here we present a theorem by means of which one can generate two Einstein-conformal scalar solutions from a single Einstein-ordinary scalar solution (of which many are known). As an example we show how to obtain Weyl-like solutions with a conformal scalar field. We obtain and analyze in some detail two families of spherically symmetric static Einstein-conformal scalar solutions. We also exhibit a family of static spherically symmetric Einstein-Maxwell-conformal scalar solutions (parametrized by both electric and scalar charge), which have black-hole geometries but are not genuine black holes. Finally, we present all the Robertson-Walker cosmological models which contain both incoherent radiation and a homogeneous conformal scalar field. One class of these represents open universes which bounce and never pass through a singular state; they circumvent the “singularity theorems” by violating the energy condition.

Relation between physical and gravitational geometry

The appearance of two geometries in a single gravitational theory is familiar. Usually, as in the Brans-Dicke theory or in string theory, these are conformally related Riemannian geometries. Is this the most general relation between the two geometries allowed by physics? We study this question by supposing that the physical geometry on which matter dynamics takes place could be Finslerian rather than just Riemannian. An appeal to the weak equivalence principle and causality then leads us to the conclusion that the Finsler geometry has to reduce to a Riemann geometry whose metric, the physical metric, is related to the gravitational metric by a generalization of the conformal transformation involving a scalar field.

Information in the Holographic Universe

Yet if we have learned anything from engineering, biology and physics, information is just as crucial an ingredient. The robot at the automobile factory is supplied with metal and plastic but can make nothing useful without copious instructions telling it which part to weld to what and so on. A ribosome in a cell in your body is supplied with amino acid building blocks and is powered by energy released by the conversion of ATP to ADP, but it can synthesize no proteins without the information brought to it from the DNA in the cells nucleus. Likewise, a century of developments in physics has taught us that information is a crucial player in physical systems and processes. Indeed, a current trend, initiated by John A. Wheeler of Princeton University, is to regard the physical world as made of information, with energy and matter as incidentals.

The modified newtonian dynamics- : MOND and its implications for new physics

No more salient issue exists in contemporary astrophysics and cosmology than that of the elusive ‘dark matter’. For many years already Milgroms paradigm of modified Newtonian dynamics (MOND) has provided an alternative way to interpret observations without appeal to invisible dark matter. MOND had been successful in elucidating economically the dynamics of disc galaxies of all scales, while doing less well for clusters of galaxies; in its original form it could not address gravitational lensing or cosmology. After reviewing some of the evidence in favour of MOND, I recollect the development of relativistic formulations for it to cope with the last deficiency. I comment on recent work by various groups in confronting TeVeS, a relativistic embodiment of MOND, with observational data on gravitational lensing and cosmology. Throughout I ask what sort of physics can be responsible for the efficacy of MOND, and conclude with an appraisal of what theoretical developments are still needed to reach a full description of the world involving no unobserved matter.

Black‐hole thermodynamics

To the physicist casually interested in gravitation, a black hole is a passive object that swallows anything near it and cannot be made to disgorge it; it absorbs but cannot emit. At the close of the last decade the experts shared this view. Recently, however, this simple picture has changed entirely. Perhaps no single development highlighted more the new views about black holes than the quantum argument presented by Stephen Hawking of Cambridge University in 1974 that a black hole must radiate spontaneously with a thermal spectrum. The importance of this phenomenon is not so much in possible practical applications, not even in its astrophysical implications, but rather in that it has confirmed earlier suspicions that gravitation, thermodynamics and the quantum world are deeply interconnected. This connection, which might be symbolized by the thermodynamic engine shown in figure 1, engenders hope that we may achieve a synthesis of these three branches of physics in our time and bears witness to the profound unity of physics, a unity too often veiled in an age of increasing specialization.To the physicist casually interested in gravitation, a black hole is a passive object that swallows anything near it and cannot be made to disgorge it; it absorbs but cannot emit. At the close of the last decade the experts shared this view. Recently, however, this simple picture has changed entirely. Perhaps no single development highlighted more the new views about black holes than the quantum argument presented by Stephen Hawking of Cambridge University in 1974 that a black hole must radiate spontaneously with a thermal spectrum. The importance of this phenomenon is not so much in possible practical applications, not even in its astrophysical implications, but rather in that it has confirmed earlier suspicions that gravitation, thermodynamics and the quantum world are deeply interconnected. This connection, which might be symbolized by the thermodynamic engine shown in figure 1, engenders hope that we may achieve a synthesis of these three branches of physics in our time and bears witness to the profou...

Gravitational-radiation recoil and runaway black holes

In the nonspherical gavitational collapse of a stellar core to a black hole, linear momentum will in general be radiated with gravitational waves. As a result the black hole will recoil. Here we make a rough estimate of the possible recoil velecities by means of the linearized theory of gravitational waves extended to ectopole order. Velocities ranging from small values for nearly up- down symmetrical collapse up to a few hundred kilometers per second for highly asymmetrical collapse may be possible. We also explore some likely consequences of black-hole recoil: breakup of a binary upon collapse of one of its components, runaway binaries with a black-hole component, detachment of the stellar envelope from the black hole formed by the collapsed stellar core, and escape of black holes from globular clusters and the Galaxy. (auth)

Black holes with scalar charge

Abstract Previously it had been thought that a stationary black hole with an exterior devoid of matter can be parametrized only by mass, angular momentum, and electric charge. We show here that scalar charge is also an admissible parameter. Our starting point is a new solution of Einsteins equations with stress-energy of electromagnetic and conformal scalar fields which we presented earlier. It has a black-hole geometry, and is parametrized by electric and scalar charges. Its conformal scalar field is unbounded at the event horizon, and we originally regarded this feature as incompatible with a black hole interpretation. However, following a suggestion of B. DeWitt, we show here that the infinity in the scalar field need not be physically pathological: it is not associated with an infinite potential barrier for test scalar charges; it does not cause the termination of any trajectories of these test particles at finite proper time; and it is not connected with unbounded tidal accelerations between neighboring trajectories. In view of these facts, we now regard the new solution as a genuine black hole solution.

No hair for spherical black holes: Charged and nonminimally coupled scalar field with self-interaction

We prove three theorems in general relativity which rule out classical scalar hair of static, spherically symmetric, possibly electrically charged black holes. We first generalize Bekensteins no-hair theorem for a multiplet of minimally coupled real scalar fields with not necessarily quadratic action to the case of a charged black hole. We then use a conformal map of the geometry to convert the problem of a charged (or neutral) black hole with hair in the form of a neutral self-interacting scalar field nonminimally coupled to gravity to the preceding problem, thus establishing a no-hair theorem for the cases with a nonminimal coupling parameter

Black holes and information theory

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