On thermodynamics of black p-branes

TL;DR

This paper investigates the semi-classical thermodynamic properties of black p-branes in D-dimensional spacetime, revealing how key quantities depend on a specific combination of dimensions and identifying a critical behavior at a certain parameter value.

Contribution

It introduces a dimension-dependent analysis of black p-brane thermodynamics, highlighting the role of the combined parameter  d and its implications for entropy and stability.

Findings

Thermodynamic quantities depend on D and d through  d=D-d-2.

Hawking temperature and lifetime vary with  d, with a critical point at  d=2.

Remnants with non-zero entropy exist for  d>2.

Abstract

Thermodynamic properties of a class of black $p$-branes in $D$-dimensions considered by Duff and Lu are investigated semi-classically. For black $(d-1)$-brane, thermodynamic quantities depend on $D$ and $d$ only through the combination $\tilde d \equiv D-d-2$. The behavior of the Hawking temperature and the lifetime vary with $\tilde d$, with a critical value $\tilde d=2$. For $\tilde d>2$, there remains a remnant, in which non-zero entropy is stored. Implications of the fact that the Bekenstein-Hawking entropy of the black $(d-1)$-brane depend only on $\tilde d=D-d-2$ is discussed from the point of view of duality.