Prospecting Black Hole Thermodynamics with Fractional Quantum Mechanics
arXiv:2107.04789 · doi:10.1140/epjc/s10052-021-09438-5
Abstract
This paper investigates whether the framework of fractional quantum mechanics can broaden our perspective of black hole thermodynamics. Concretely, we employ a {\it space-fractional} derivative \cite{Rie} as our main tool. Moreover, we restrict our analysis to the case of a Schwarzschild configuration. From a subsequently modified Wheeler-DeWitt equation, we retrieve the corresponding expressions for specific observables. Namely, the black hole mass spectrum, , its temperature , and entropy, . We find that these bear consequential alterations conveyed through a fractional parameter, . In particular, the standard results are recovered in the specific limit . Furthermore, we elaborate how generalizations of the entropy-area relation suggested by Tsallis and Cirto \cite{Tsallis} and Barrow \cite{Barrow} acquire a complementary interpretation in terms of a fractional point of view. A thorough discussion of our results is presented.
13 pages,2 figures, 1 table, to appear in EPJC
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