On the nature of black hole entropy

I share some memories and offer a personal perspective on Jacob Bekenstein's legacy, focussing on black hole entropy and the Bekenstein bound. I summarize a number of fascinating recent developments that grew out of Bekenstein's pioneering contributions, from the Ryu-Takayanagi proposal to the Quantum Null Energy Condition.

I review some recent work in which the quantum states of string theory which are associated with certain black holes have been identified and counted. For large black holes, the number of states turns out to be precisely the exponential of the Bekenstein-Hawking entropy. This provides a statistical origin for black hole thermodynamics in the context of a potential quantum theory of gravity.

We discuss the most interesting approaches to derivation of the Bekenstein-Hawking entropy formula from a statistical theory.

This is an introductory, up-to-date review of the essentials of black hole thermodynamics. The main topics surveyed are: (i) the four laws of thermodynamics as applied to a black hole horizon, and the current status of their proofs; (ii) different definitions of horizons, and their unique properties; (iii) the nature of black hole entropy, its quantum and stringy corrections, and ultimate origin from quantum gravity microstates; (iv) the focusing law for the area/entropy; and...

Black holes are a continuing source of mystery. Although their classical properties have been understood since the 1970's, their quantum properties raise some of the deepest questions in theoretical physics. Some of these questions have recently been answered using string theory. I will review these fundamental questions, and the aspects of string theory needed to answer them. I will then explain the recent developments and new insights into black holes that they provide. Som...

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, fix...

In the talk different definitions of the black hole entropy are discussed and compared. It is shown that the Bekenstein-Hawking entropy $S^{BH}$ (defined by the response of the free energy of a system containing a black hole on the change of the temperature) differs from the statistical- mechanical entropy $S^{SM}=-\mbox{Tr}(\hat{\rho}\ln \hat{\rho})$ (defined by counting internal degrees of freedom of a black hole). A simple explanation of the universality of the Bekenstein-...

We discuss and compare different definitions of the entropy of a black hole. In particular we show that the thermodynamical entropy defined by the response of the free energy of a black hole to the change of temperature does not coincide with the statistical-mechanical entropy, obtained by counting its dynamical degrees of freedom. The no-boundary wavefunction of a black hole, its relation to the entropy problem and its generalization are discussed. We discuss the relation be...

We review some recent advances in black hole thermodynamics, including statistical mechanical origins of black hole entropy and its leading order corrections, from the viewpoints of various quantum gravity theories. We then examine the information loss problem and some possible approaches to its resolution. Finally, we study some proposed experiments which may be able to provide experimental signatures of black holes.

Black holes have their own thermodynamics including notions of entropy and temperature and versions of the three laws. After a light introduction to black hole physics, I recollect how black hole thermodynamics evolved in the 1970's, while at the same time stressing conceptual points which were given little thought at that time, such as why the entropy should be linear in the black hole's surface area. I also review a variety of attempts made over the years to provide a stati...