2023/05/31 by I. Ya. Aref’eva, Aref'eva, I. Ya., I. V. Volovich +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.2305.19827
openalex publication_date 2023/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Black holes violate the third law of thermodynamics, and this gives rise to difficulties with the microscopic description of the entropy of black holes. Recently, it has been shown that the microscopic description of the Schwarzschild black hole thermodynamics in D = 4 spacetime dimensions is provided by the analytical continuation of the entropy of Bose gas with non-relativistic one particle energy to d =-4 negative spatial dimension. In this paper, we show that the D=5 and D=6 Schwarzschild black holes thermodynamics can be modeled by the d-dimensional Bose gas, d=1,2,3..., with the one particle energy ε(k)=kα under conditions α=-d/3 and α=-d/4, respectively. In these cases the free energy of the Bose gas has divergences and we introduce a cut-off and perform the minimal renormalizations. We also perform renormalizations using analytical regularization and prove that the minimal cut-off renormalization gives the same answer as the analytical regularization by the Riemann zeta-function.