On the Bekenstein-Hawking Entropy, Non-Commutative Branes and Logarithmic Corrections

TL;DR

This paper generalizes the derivation of Bekenstein-Hawking entropy to higher-dimensional spacetimes involving dual brane pairs, incorporating non-commutative effects and revealing a universal logarithmic correction with a specific prefactor.

Contribution

It extends previous work to higher dimensions, showing the state counting mechanism applies to all dual brane pairs and naturally includes non-commutative effects and logarithmic corrections.

Findings

Validates the state counting for all dual brane pairs in higher dimensions.

Incorporates non-commutativity on brane worldvolumes into entropy derivation.

Derives a universal logarithmic correction with prefactor 1/2.

Abstract

We extend earlier work on the origin of the Bekenstein-Hawking entropy to higher-dimensional spacetimes. The mechanism of counting states is shown to work for all spacetimes associated with a Euclidean doublet $(E_1,M_1)+(E_2,M_2)$ of electric-magnetic dual brane pairs of type II string-theory or M-theory wrapping the spacetime's event horizon plus the complete internal compactification space. Non-Commutativity on the brane worldvolume enters the derivation of the Bekenstein-Hawking entropy in a natural way. Moreover, a logarithmic entropy correction with prefactor 1/2 is derived.