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.