On the Existence of the Logarithmic Correction Term in Black Hole Entropy-Area Relation

TL;DR

This paper investigates how the number of spacetime dimensions influences the presence of a logarithmic correction in black hole entropy, revealing that such corrections appear only in even-dimensional universes within a modified entropy-area framework.

Contribution

It establishes a link between spacetime dimensionality and the logarithmic correction term in black hole entropy using the generalized uncertainty principle.

Findings

Logarithmic prefactor appears only in even dimensions

Modified entropy-area relation depends on spacetime dimensions

Analysis restricted to microcanonical ensembles

Abstract

In this paper we consider a model universe with large extra dimensions to obtain a modified black hole entropy-area relation. We use the generalized uncertainty principle to find a relation between the number of spacetime dimensions and the presence or vanishing of logarithmic prefactor in the black hole entropy-area relation. Our calculations are restricted to the microcanonical ensembles and we show that in the modified entropy-area relation, the microcanonical logarithmic prefactor appears only when spacetime has an even number of dimensions.