The Bekenstein-Hawking entropy or black hole entropy is the amount of entropy that must be assigned to a black hole in order for it to comply with the laws of thermodynamics as they are interpreted by observers external to that black hole. This is particularly true for the first and second laws. Black hole entropy is a concept with geometric root but with many physical consequences. It ties together notions from gravitation, thermodynamics and quantum theory, and is thus regarded as a window into the as yet mostly hidden world of quantum gravity.

Why black hole entropy?

A black hole may be described as a blemish in spacetime, or a locale of very high curvature. Is it meaningful or desirable to associate entropy with it ? Is this possible at all ?

There are several ways to justify the concept of black hole entropy (Bekenstein 1972, 1973).

  • A black hole is usually formed from the collapse of a quantity of matter or radiation, both of which carry entropy. However, the hole’s interior and contents are veiled to an exterior observer. Thus a thermodynamic description of the collapse from that observer’s viewpoint cannot be based on the entropy of that matter or radiation because these are unobservable. Associating entropy with the black hole provides a handle on the thermodynamics.
  • A stationary black hole is parametrized by just a few numbers (Ruffini and Wheeler 1971): its mass, electric charge and angular momentum (and magnetic monopole charge, except its actual existence in nature has not been demonstrated yet). For any specific choice of these parameters one can imagine many scenarios for the black hole’s formation. Thus there are many possible internal states corresponding to that black hole. In thermodynamics one meets a similar situation: many internal microstates of a system are all compatible with the one observed (macro)state. Thermodynamic entropy quantifies the said multiplicity. Thus by analogy one needs to associate entropy with a black hole .
  • By blocking all signal travel through it, the event horizon prevents an external observer from receiving information about the black hole. Thus a black hole can be said to hide information. In ordinary physics entropy is a measure of missing information. Hence it makes sense to attribute entropy to a black hole.

More on this: