![]() ![]() In 1972, Jacob Bekenstein conjectured that black holes should have an entropy, where by the same year, he proposed no-hair theorems. The increase of the entropy of the black hole more than compensates for the decrease of the entropy carried by the object that was swallowed. If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole. The second law of thermodynamics requires that black holes have entropy. S_Q^2/c^2)^2-(J/Mc)^2=0.An artist's depiction of two black holes merging, a process in which the laws of thermodynamics are upheld Overview If \(A\) stands for the surface area of a black hole (area of the event horizon), then the black hole entropy, in dimensionless form, is given by Thus it is reasonable that the black hole entropy should be a monotonic function of area, and it turns out to be simplest such function. This increasing behavior is reminiscent of thermodynamic entropy of closed systems. One way to understand why is to recall the "area theorem" (Hawking 1971, Misner, Thorne and Wheeler 1973): the event horizon area of a black hole cannot decrease it increases in most transformations of the black hole. It turns out that these three parameters enter only in the same combination as that which represents the surface area of the black hole. How to express the black hole entropy in a concrete formula? It is clear at the outset that black hole entropy should only depend on the observable properties of the black hole: mass, electric charge and angular momentum. Hence it makes sense to attribute entropy to a black hole. In ordinary physics entropy is a measure of missing information. Thus a black hole can be said to hide information.
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