https://doi.org/10.1140/epjp/s13360-025-06306-z
Regular Article
Entropy of black holes, charged probes and noncommutative generalization
Rudjer Bošković Institute, Bijenčka c.54, HR-10002, Zagreb, Croatia
Received:
12
December
2024
Accepted:
5
April
2025
Published online:
20
May
2025
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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
