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arXiv · 2107.04789

Prospecting Black Hole Thermodynamics with Fractional Quantum Mechanics

S. Jalalzadeh·F. Rodrigues da Silva·P. V. Moniz
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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.

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S. Jalalzadeh, F. Rodrigues da Silva, P. V. Moniz. 2021-07-10. Prospecting Black Hole Thermodynamics with Fractional Quantum Mechanics. https://doi.org/10.1140/epjc%2Fs10052-021-09438-5

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