Black hole entropy

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The proposal, made by Jacob Bekenstein in the early 1970s and given its coefficient by Hawking's 1974 temperature, that a black hole carries entropy proportional to the area of its horizon rather than to any volume. It resolved an apparent violation of the second law - throw a hot gas into a black hole and the entropy of the universe seems to fall - by giving the hole an entropy of its own that necessarily rises. The numbers are extreme: a solar-mass black hole carries an entropy some twenty orders of magnitude larger than the star that formed it, which is another way of saying that almost all the information about that star has become inaccessible. Because the quantity scales with area and not volume, it is the origin of the holographic principle, the suggestion that the degrees of freedom of a region can be accounted for on its boundary. String theory reproduced the exact coefficient for certain highly symmetric extremal black holes in 1996, which is regarded as a genuine success; the general case is not derived. Not a place on Earth.

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