2024/07/18 by Axel Hrelja, Tajron Jurić, Hrelja, Axel +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2407.13233
openalex publication_date 2024/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The brick wall model is a semi-classical approach to understanding the microscopic origin of black hole entropy. We outline the formalism for the brick wall model in arbitrary number of dimensions and generalize it to include both charged spacetimes and charged probes in order to systematically show how to calculate the entropy for any black hole, in higher orders of the WKB approximation. We calculate the entropy for the Reissner-Nordström and charged BTZ black holes, and by looking at the chargeless limits we recover the entropy of the Schwarzschild and neutral BTZ black holes. We also study noncommutative corrections to the black hole entropy by using a Drinfeld twist to deform spacetime symmetries. Using the noncommutative action for a charged scalar field, we derive the noncommutative Klein-Gordon equation and the radial equation in arbitrary dimension on which we generalize the brick wall method. We study case by case the noncommutative Reissner-Nordström and noncommutative charged BTZ black holes, the entropy of which we calculate using the generalized brick wall method. Corrections due to higher order in the WKB approximation arise, and they are given by the logarithms of the black hole area. The corrections in the lowest order of WKB due to noncommutativity are also given by the logarithms of the black hole area.