High-Order Corrections to the Entropy and Area of Quantum Black Holes

TL;DR

This paper investigates potential small corrections to the black hole area-entropy relation, ruling out power-law corrections and constraining logarithmic ones, with implications for quantum black hole models.

Contribution

It provides the first rigorous constraints on possible logarithmic corrections to black hole entropy and explores their implications for the area-mass relation.

Findings

Power-law corrections are ruled out.

Severe constraints on log-area correction coefficients.

Logarithmic corrections imply modifications to the area-mass relation.

Abstract

The celebrated area-entropy formula for black holes has provided the most important clue in the search for the elusive theory of quantum gravity. We explore the possibility that the (linear) area-entropy relation acquires some smaller corrections. Using the Boltzmann-Einstein formula, we rule out the possibility for a power-law correction, and provide severe constraints on the coefficient of a possible log-area correction. We argue that a non-zero logarithmic correction to the area-entropy relation, would also imply a modification of the area-mass relation for quantum black holes.