Disturbing the Black Hole

I describe some examples in support of the conjecture that the horizon area of a near equilibrium black hole is an adiabatic invariant. These include a Schwarzschild black hole perturbed by quasistatic scalar fields (which may be minimally or nonminimally coupled to curvature), a Kerr black under the influence of scalar radiation at the superradiance treshold, and a Reissner--Nordstr\"om black hole absorbing a charge marginally. These clarify somewhat the conditions under which the conjecture would be true. The desired ``adiabatic theorem'' provides an important motivation for a scheme for black hole quantization.Comment: 15 pages, LaTeX with crckapb style, to appear in ``The Black Hole Trail'', eds. B. Bhawal and B. Iyer (Kluwer, Dordrecht 1998

Black Holes: Classical Properties, Thermodynamics and Heuristic Quantization

I discuss the no hair principle, the recently found hairy solutions, generic properties of nonvacuum spherical static black holes, and the new no scalar hair theorems. I go into the generic phenomenon of superradiance, first uniform linear motion superradiance, then Kerr black hole superradiance, and finally general rotational superradiance and its possible applications in the laboratory. I show that the horizon area of a nearly stationary black hole can be regarded as an adiabatic invariant. This invariance suggests that quantum horizon area is quantized in multiples of a basic unit. Consideration of the quantum version of the Christodoulou reversible processes provides support for this idea. Horizon area quantization dictates a definite discrete black hole mass spectrum, so that Hawking's semiclassical spectrum is predicted to be replaced by a spectrum of nearly uniformly spaced lines whose envelope is roughly Planckian. Line natural broadening seems not enough to wash out the lines. To check on the possibility of line splitting, I present a simple algebra involving, among other operators, the black hole observables. Under simple assumptions it also leads to the uniformly spaced area spectrum.Comment: LaTeX, 44 pages, 4 eps figs. and conf_cg.sty included. Lectures delivered at the IX Brazilian School on Cosmology and Gravitation, Rio de Janeiro 7-8/98. Updated references and positioning on page correcte

Black hole hair: twenty--five years after

Originally regarded as forbidden, black hole ``hair'' are fields associated with a stationary black hole apart from the gravitational and electromagnetic ones. Several stable stationary black hole solutions with gauge or Skyrme field hair are known today within general relativity. We formulate here a ``no scalar--hair'' conjecture, and adduce some new theorems that almost establish it by ruling out - for all but a small parameter range - scalar field hair of spherical black holes in general relativity, whether the field be self--interacting, coupled to an Abelian gauge field, or nonminimally coupled to gravity.Comment: 6 pages, Latex, Invited talk at the Second Sakharov Conference in Physics, Moscow, May 20-24, 1996; briefer version to appear in the proceeding

Optimizing entropy bounds for macroscopic systems

The universal bound on specific entropy was originally inferred from black hole thermodynamics. We here show from classical thermodynamics alone that for a system at fixed volume or fixed pressure, the ratio of entropy to nonrelativistic energy has a unique maximum $(S/E)_\mathrm{max}$. A simple argument from quantum dynamics allows one to set a model--independent upper bound on $(S/E)_\mathrm{max}$ which is usually much tighter than the universal bound. We illustrate with two examples.Comment: 13 pages, 2 figures, LaTe

Limitations on quantum information from black hole physics

After reviewing the relation of entropy to information, I derive the entropy bound as applied to bounded weakly gravitating systems, and review the bound's applications to cosmology as well as its extensions to higher dimensions. I then discuss why black holes behave as 1-D objects when emitting entropy, which suggests that a black hole swallows information at a rate restricted by the one-channel information capacity. I discuss fundamental limitations on the information borne by signal pulses in curved spacetime, from which I verify the mentioned bound on the rate of information disposal by a black hole.Comment: LaTeX, 14 pages. Lecture delivered at XXV International School of Theoretical Physics, Ustron, Poland, Sep. 10-16, 2001 (proceedings edited by M. Biesiada to appear in Acta Physica Polonica B). It is an abridged streamlined version of one of my Erice (2001) lectures, gr-qc/010704

Preparing the State of a Black Hole

Measurements of the mass or angular momentum of a black hole are onerous, particularly if they have to be frequently repeated, as when one is required to transform a black hole to prescribed parameters. Irradiating a black hole of the Kerr-Newman family with scalar or electromagnetic waves provides a way to drive it to prescribed values of its mass, charge and angular momentum without the need to repeatedly measure mass or angular momentum throughout the process. I describe the mechanism, which is based on Zel'dovich-Misner superradiance and its analog for charged black holes. It represents a possible step in the development of preparation procedures for quantum black holes.Comment: Essay in honor of Mario Novello's sixtieth birthday. LaTeX 209, 12 pages, no figure

Relativistic gravitation theory for the MOND paradigm

The modified newtonian dynamics (MOND) paradigm of Milgrom can boast of a number of successful predictions regarding galactic dynamics; these are made without the assumption that dark matter plays a significant role. MOND requires gravitation to depart from Newtonian theory in the extragalactic regime where dynamical accelerations are small. So far relativistic gravitation theories proposed to underpin MOND have either clashed with the post-Newtonian tests of general relativity, or failed to provide significant gravitational lensing, or violated hallowed principles by exhibiting superluminal scalar waves or an \textit{a priori} vector field. We develop a relativistic MOND inspired theory which resolves these problems. In it gravitation is mediated by metric, a scalar field and a 4-vector field, all three dynamical. For a simple choice of its free function, the theory has a Newtonian limit for nonrelativistic dynamics with significant acceleration, but a MOND limit when accelerations are small. We calculate the $\beta$ and $\gamma$ PPN coefficients showing them to agree with solar system measurements. The gravitational light deflection by nonrelativistic systems is governed by the same potential responsible for dynamics of particles. To the extent that MOND successfully describes dynamics of a system, the new theory's predictions for lensing by that system's visible matter will agree as well with observations as general relativity's predictions made with a dynamically successful dark halo model. Cosmological models based on the theory are quite similar to those based on general relativity; they predict slow evolution of the scalar field. For a range of initial conditions, this last result makes it easy to rule out superluminal propagation of metric, scalar and vector waves.Comment: ReVTeX and 3 eps figures; 34 pages; postpublication replacement with some corrections to Secs.IV.A+C, V and Appendix D (incorporates erratum Phys. Rev. D71, 069901(E) (2005)

Holographic Bound from Second Law

The holographic bound that the entropy (log of number of quantum states) of a system is bounded from above by a quarter of the area of a circumscribing surface measured in Planck areas is widely regarded a desideratum of any fundamental theory, but some exceptions occur. By suitable black hole gedanken experiments I show that the bound follows from the generalized second law for two broad classes of isolated systems: generic weakly gravitating systems composed of many elementary particles, and quiescent, nonrotating strongly gravitating configurations well above Planck mass. These justify an early claim by Susskind.Comment: Invited talk at Marcel Grossman IX meeting in Rome, July 2000; improved version of Phys. Lett. B 481, 339 (2000). 7 pages, LaTeX with included mprocl.st

An alternative to the dark matter paradigm: relativistic MOND gravitation

MOND, invented by Milgrom, is a phenomenological scheme whose basic premise is that the visible matter distribution in a galaxy or cluster of galaxies alone determines its dynamics. MOND fits many observations surprisingly well. Could it be that there is no dark matter in these systems and we witness rather a violation of Newton's universal gravity law ? If so, Einstein's general relativity would also be violated. For long conceptual problems have prevented construction of a consistent relativistic substitute which does not obviously run afoul of the facts. Here I sketch TeVeS, a tensor-vector-scalar field theory which seems to fit the bill: it has no obvious conceptual problems and has a MOND and Newtonian limits under the proper circumstances. It also passes the elementary solar system tests of gravity theory.Comment: 18 pages, invited talk at the 28th Johns Hopkins Workshop on Current Problems in Particle Theory, June 2004, Johns Hopkins University, Baltimore. Corrections to Sec.7 for error pointed out by D. Giannios. To appear online in JHEP Proceedings of Scienc

Do We Understand Black Hole Entropy ?

I review various proposals for the nature of black hole entropy and for the mechanism behind the operation of the generalized second law. I stress the merits of entanglement entropy {\tenit qua\/} black hole entropy, and point out that, from an operational viewpoint, entanglement entropy is perfectly finite. Problems with this identification such as the multispecies problem and the trivialization of the information puzzle are mentioned. This last leads me to associate black hole entropy rather with the multiplicity of density operators which describe a black hole according to exterior observers. I relate this identification to Sorkin's proof of the generalized second law. I discuss in some depth Frolov and Page's proof of the same law, finding it relevant only for scattering of microsystems by a black hole. Assuming that the law is generally valid I make evident the existence of the universal bound on entropy regardless of issues of acceleration buoyancy, and discuss the question of why macroscopic objects cannot emerge in the Hawking radiance.Comment: plain TeX, 18 pages, Plenary talk at Seventh Marcel Grossman meeting at Stanford University, gr-qc/9409015, revised to include a figur