nLab
Bekenstein-Hawking entropy

Context

Gravity

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

In gravity, Bekenstein-Hawking entropy is an entropy assigned to black hole, on the basis of laws of thermodynamics and observers outside black hole. It striking property is that it is proportional to the surface area of the balck hole’s horizon.

Properties

Interpretation in AdS/CFT correspondence

In the context of string theory BH entropy is explained by a version of the AdS/CFT correspondence. Here every black brane solution in supergravity is the strong-coupling limit of a D-brane worldvolume QFT. After KK-reduction these black brane configurations become ordinary black holes. The entropy of the D-brane worldvolume theories on the event horizon turns out to coincide with the BH entropy of the corresponding black hole.

Detailed computations exist in particular for D1-brane/D5-brane systems. This is parts of the AdS/CFT correspondence. See (AGMOO, chapter 5).

See also string theory results applied elsewhere.

Interpretation by strong coupling limit of D-branes

Another way to derive Bekenstein-Hawking entropy in string theory is by computing the entropy of weakly coupled open strings on D-brane configurations in flat Minkowski space which transmute as the coupling constant is increased to given (supersymmetric) black hole configurations. More on this is at black holes in string theory.

References

General

Basic introductory accounts include

A more general discussion which identifies thermodynamic properties of all horizons appearing on gravity (not just black hole horizons) was given in

This article showed that under some assumptions the Einstein equations can even be derived from identifying gravitational horizon area with entropy and them imposing laws of thermodynamics.

For more comments and more references on this observation see

(Later authors tried to argue that derivations like this show that gravity is not a fundamental force of nature such as electromagnetism or the strong nuclear force, but rather an entropic force that arises only from more fundamental forces in a thermodynamic limit. This however remains at best unclear.)

Discussion of black hole entropy from entropy of conformal field theory associated with the horizon has been given in

and reviewed in

Further developments on black hole entropy are in

A related controversial article that spawned a lot of discussion is

Interpretation in string theory

A survey of interpretation of black holes in string theory is in Chapter 5 of

See also

Interpretation as entanglement entropy

Discussions of the interpreation of BH entropy as entanglement entropy include

Revised on March 17, 2014 02:07:51 by Urs Schreiber (89.204.154.159)