Generalized first law of thermodynamics for black holes in spacetimes which are not asymptotically flat

Physics

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Scientific paper

The general formulation of the first law of thermodynamics for static or stationary black holes in spacetimes which are not asymptotically flat is derived. The only difference between the first law given here and Bardeen, Carter and Hawking's first law (BCH first law) is that the mass M of the black hole in BCH's first law is replaced by the total energy E of the system. This is because the mass and energy of a black hole whose spacetime is not asymptotically flat are not identical to those of a black hole whose spacetime is asymptotically flat. The first law given here is also valid for a black hole whose spacetime is asymptotically flat.

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