Abstract
This paper investigates whether the framework of fractional quantum mechanics can broaden our perspective of black hole thermodynamics. Concretely, we employ a space-fractional derivative (Riesz in Acta Math 81:1, 1949) 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 (Eur Phys J C 73:2487, 2013) and Barrow (Phys Lett B 808:135643, 2020) acquire a complementary interpretation in terms of a fractional point of view. A thorough discussion of our results is presented.
Highlights
On the other hand, innovative work on Black hole (BH) physics in the past forty years or so have brought us to the forefront of unanticipated research directions
Thereafter, physicists realized an intimate connection between geometrical horizons, thermodynamic temperature and quantum mechanics [17,18,19]
This shows that the leading term of the Fractional Quantum Mechanics (FQM) computed BH entropy can be expressed in terms of the Tsallis and Cirto result for a BH
Summary
Innovative work on BH physics in the past forty years or so have brought us to the forefront of unanticipated research directions. A set of pertinent arguments and results have been put forward to apply fractional calculus [30,31,32,33,34,35] in quantum physics Such framework is known as Fractional Quantum Mechanics (FQM), see e.g. The essential motivation for FQM emerges in that if we restrict the path integral (Feynman) description of quantum mechanics to Brownian paths only, it will be challenging to explain a few other pertinent quantum phenomena [41] Such difficulties have led to consider a generalization of the Feynman path integral, by replacing the Gaussian probability distribution by Lévy’s [42]; the Hausdorff dimension of the Lévy path is equal to the fractional parameter α.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
