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:
https://blogs.scientificamerican.com/cocktail-party-physics/in-memoriam-jacob-bekenstein-1947-2015-and-black-hole-entropy/
https://blogs.scientificamerican.com/cocktail-party-physics/in-memoriam-jacob-bekenstein-1947-2015-and-black-hole-entropy/
