Universal canonical black hole entropy

TL;DR

This paper demonstrates that non-rotating black holes in three and four dimensions have a universal entropy following the Bekenstein-Hawking law with a logarithmic correction, assuming a specific quantum spectrum relation.

Contribution

It establishes a universal correction to black hole entropy based on quantum spectrum assumptions within Canonical Quantum General Relativity.

Findings

Entropy obeys Bekenstein-Hawking law with logarithmic correction

Universal negative coefficient for the correction term

Thermal instability linked to the quantum spectrum index

Abstract

Non-rotating black holes in three and four dimensions are shown to possess a canonical entropy obeying the Bekenstein-Hawking area law together with a leading correction (for large horizon areas) given by the logarithm of the area with a {\it universal} finite negative coefficient, provided one assumes that the quantum black hole mass spectrum has a power law relation with the quantum area spectrum found in Non-perturbative Canonical Quantum General Relativity. The thermal instability associated with asymptotically flat black holes appears in the appropriate domain for the index characterising this power law relation, where the canonical entropy (free energy) is seen to turn complex.