Black Holes: Insights and Enigmas

An elementary introduction is given to the problem of black hole entropy as formulated by Bekenstein and Hawking, based on the so-called Laws of Black Hole Mechanics. Wheeler's 'It from Bit' picture is presented as an explanation of plausibility of the Bekenstein-Hawking Area Law. A variant of this picture that takes better account of the symmetries of general relativity is shown to yield corrections to the Area Law that are logarithmic in the horizon area, with a finite, fixed coefficient. The Holographic hypothesis, tacitly assumed in the above considerations, is briefly described and the beginnings of a general proof of the hypothesis is sketched, within an approach to quantum gravitation which is non-perturbative in nature, namely Non-perturbative Quantum General Relativity (also known as Quantum Geometry). The holographic entropy bound is shown to be somewhat tightened due to the corrections obtained earlier. A brief summary of Quantum Geometry approach is included, with a sketch of a demonstration that precisely the log area corrections obtained from the variant of the It from Bit picture adopted earlier emerges for the entropy of generic black holes within this formalism.

Since Karl Schwarzschild in 1915 discovered that the distance from the center of an object, where all the mass of the object were compressed within a symmetrically sphere, the escape speed from the surface would equal the speed of light. This distance is known as the Schwarzschild radius. Such an object -further called black hole -would be formed from the collapse of at least 3 solar masses, and would not allow anything to come out of it, not even light. In the seventies Jacob Bekenstein and Stephen Hawking calculated the entropy of such a black hole. Hawking also proposed that black holes actually radiate, and eventually evaporate. In the nineties string theory could also be used to calculate black hole entropy.

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 2005

I present a viewpoint on black hole thermodynamics according to which the entropy: derives from horizon "degrees of freedom"; is finite because the deep structure of spacetime is discrete; is "objective" thanks to the distinguished coarse graining provided by the horizon; and obeys the second law of thermodynamics precisely because the effective dynamics of the exterior region is not unitary. Probably few people doubt that the twin phenomena of black hole entropy and evaporation hold important clues to the nature of quantum spacetime, but the agreement pretty much ends there. Starting from the same evidence, different workers have drawn very different, and partly contradictory, lessons. On one hand, there is perhaps broad agreement that the finiteness of the entropy points to an element of discreteness in the deep structure of spacetime. On the other hand there is sharp disagreement over whether the thermal nature of the Hawking radiation betokens an essential failure of unitarity in quantum gravity or whether it is instead betraying the need for a radical revision of the spacetime framework, as contemplated for instance in the "holographic principle". These alternatives are not necessarily in contradiction, of course, but in practice, the wish to retain unitarity has been one of the strongest motivations for taking seriously the latter type of possibility. My own belief is that non-unitarity is probably inevitable in connection with gravity and that, rather than shunning this prospect, we ought to welcome it because it offers a straightforward way to understand why the law of entropy increase continues to hold in the presence

Cambridge Review, 1980

An explanation of what Hawking's formula for the entropy of a black holes is all about. Article published in the Cambridge Review 37 years ago. I have spent much time since then working out the ideas expressed in this article.

2006

2014

Black holes, thermodynamics and entropy are three topics which both separately and together raise several quite deep and serious questions which need to be addressed. Here an attempt is made to highlight some of these issues and to indicate a possible linkage between the accepted entropy expression for a black hole and the paradox linked to black holes and information loss.

arXiv (Cornell University), 2015

2024

We construct an infinite family of microstates for black holes in Minkowski spacetime which have effective semiclassical descriptions in terms of collapsing dust shells in the black hole interior. Quantum mechanical wormholes cause these states to have exponentially small, but universal, overlaps. We show that these overlaps imply that the microstates span a Hilbert space of log dimension equal to the event horizon area divided by four times the Newton constant, explaining the statistical origin of the Bekenstein-Hawking entropy.

Journal of Physics & Optics Sciences

At the present time, black holes are reduced to the parameters of the Schwarzschild sphere. It is shown that Schwarzschild determined only half of the mass and energy of a black hole, and its spherical shape makes it difficult to interact with the external environment. The elimination of this drawback is the main goal of this work, and the substantiation of the shape, structure and parameters of black holes on the basis of the strict laws of the material world is its scientific novelty. The Methods of Research: Used in the work are based on deduction and induction, as well as on the application of reliable laws of physics and the general principles of the theory of knowledge. Work Results: It is proposed to replace the Schwarzschild sphere at the quantum level of the material world with a hole-die, which consists of 2 layers of hexagonal prisms of circular space quanta, formed from 6 regular trihedral prisms of elementary space quanta. The length of all their faces is λG =4.05126∙10...

Physics Letters B, 2003

We consider a model of a black hole consisting of a number of elementary components. Examples of such models occur in the Ashtekar's approach to canonical Quantum Gravity and in M-theory. We show that treating the elementary components as completely distinguishable leads to the area law for the black hole entropy. Contrary to previous results, we show that no Bose condensation occurs, the area has big local fluctuations and that in the framework of canonical Quantum Gravity the area of the black hole horizon is equidistantly quantized.