A Complementary Third Law for Black Hole Thermodynamics

Abstract

There are some examples in the literature, in which despite the fact that the underlying theory or model does not impose a lower bound on the size of black holes, the final temperature under Hawking evaporation is nevertheless finite and nonzero. We show that under some loose conditions, the black hole is necessarily an effective remnant, in the sense that its evaporation time is infinite. That is, the final state that there is nonzero finite temperature despite having no black hole remaining cannot be realized. We discuss the limitations, subtleties, and the implications of this result, which is reminiscent of the third law of black hole thermodynamics, but with the roles of temperature and size interchanged. We therefore refer to our result as the "complementary third law" for black hole thermodynamics.

arXiv comment10 pages, 5 figures; improved and published version

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• Black Hole Remnant in Massive Gravity
• The third law of thermodynamics, non-extensivity, and energy definition in black hole physics
• Charged Particle Production Rate from Cosmic Censorship in Dilaton Black Hole Spacetimes
• Thermodynamics of a Schwarzschild black hole surrounded by quintessence in the generalized uncertainty principle framework
• Gauss-Bonnet entropy and thermal dynamics of RN-AdS black holes