Prospecting Black Hole Thermodynamics with Fractional Quantum Mechanics

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, $M$, its temperature $T$, and entropy, $S$. We find that these bear consequential alterations conveyed through a fractional parameter, $\alpha$. In particular, the standard results are recovered in the specific limit $\alpha =2$. 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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Cited by in corpus (2)

• Cosmology under the fractional calculus approach
• Quantum Cosmology in $f(Q)$ theory