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Article

Statistical Entropy Based on the Generalized-Uncertainty- Principle-Induced Effective Metric

1
Center for Quantum Spacetime, Sogang University, Seoul 04107, Republic of Korea
2
Department of Physics, Sogang University, Seoul 04107, Republic of Korea
3
Research Institute of Physics and Chemistry, Jeonbuk National University, Jeonju 54896, Republic of Korea
4
Department of Physics, Jeonbuk National University, Jeonju 54896, Republic of Korea
*
Author to whom correspondence should be addressed.
Universe 2025, 11(8), 256; https://doi.org/10.3390/universe11080256 (registering DOI)
Submission received: 9 June 2025 / Revised: 18 July 2025 / Accepted: 31 July 2025 / Published: 2 August 2025
(This article belongs to the Collection Open Questions in Black Hole Physics)

Abstract

We investigate the statistical entropy of black holes within the framework of the generalized uncertainty principle (GUP) by employing effective metrics that incorporate leading-order and all-order quantum gravitational corrections. We construct three distinct effective metrics induced by the GUP, which are derived from the GUP-corrected temperature, entropy, and all-order GUP corrections, and analyze their impact on black hole entropy using ’t Hooft’s brick wall method. Our results show that, despite the differences in the effective metrics and the corresponding ultraviolet cutoffs, the statistical entropy consistently satisfies the Bekenstein–Hawking area law when expressed in terms of an invariant (coordinate-independent) distance near the horizon. Furthermore, we demonstrate that the GUP naturally regularizes the ultraviolet divergence in the density of states, eliminating the need for artificial cutoffs and yielding finite entropy even when counting quantum states only in the vicinity of the event horizon. These findings highlight the universality and robustness of the area law under GUP modifications and provide new insights into the interplay between quantum gravity effects and black hole thermodynamics.
Keywords: generalized uncertainty principle (GUP); brick wall method; black hole entropy; effective metric generalized uncertainty principle (GUP); brick wall method; black hole entropy; effective metric

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MDPI and ACS Style

Hong, S.-T.; Kim, Y.-W.; Park, Y.-J. Statistical Entropy Based on the Generalized-Uncertainty- Principle-Induced Effective Metric. Universe 2025, 11, 256. https://doi.org/10.3390/universe11080256

AMA Style

Hong S-T, Kim Y-W, Park Y-J. Statistical Entropy Based on the Generalized-Uncertainty- Principle-Induced Effective Metric. Universe. 2025; 11(8):256. https://doi.org/10.3390/universe11080256

Chicago/Turabian Style

Hong, Soon-Tae, Yong-Wan Kim, and Young-Jai Park. 2025. "Statistical Entropy Based on the Generalized-Uncertainty- Principle-Induced Effective Metric" Universe 11, no. 8: 256. https://doi.org/10.3390/universe11080256

APA Style

Hong, S.-T., Kim, Y.-W., & Park, Y.-J. (2025). Statistical Entropy Based on the Generalized-Uncertainty- Principle-Induced Effective Metric. Universe, 11(8), 256. https://doi.org/10.3390/universe11080256

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