Microstates and statistical entropy of observed 4D black holes

Institute of Theoretical and Applied Research, Duy Tan University - Hanoi 100000, Vietnam and School of Engineering and Technology, Duy Tan University - Da Nang 550000, Vietnam

Received: 22 July 2025
Accepted: 17 December 2025

Abstract

We aim to provide a microscopic explanation of observed 4D black holes based on the compactification of 5D Einstein gravity plus a positive cosmological constant on a circle. The framework of the dimensional reduction in this work allows us to compute the statistical entropy of general 4D black holes independent of the symmetries of the black hole solution, such as the spherical symmetry, and going beyond the class of special black holes that are supersymmetric and (near-)extremal as well as have exotic charges. The statistical entropy of 4D black holes includes the Bekenstein-Hawking area term at leading order and sub-leading exponential corrections. We find a new exponential correction that is more meaningful than those previously found in the literature.