Entropy and Temperature of Black 3-Branes

TL;DR

This paper investigates the entropy and temperature of near-extremal black 3-branes in type IIB supergravity, comparing gravitational entropy with string theory microstate counting, and explores solutions with momentum density.

Contribution

It demonstrates the agreement between supergravity entropy and string microstate counting up to a factor, and constructs new solutions with momentum density on 3-branes.

Findings

Supergravity entropy matches string microstate counting up to a factor.

Constructed supergravity solutions with finite momentum density on 3-branes.

Found extremal momentum-carrying 3-branes have zero horizon area.

Abstract

We consider slightly non-extremal black 3-branes of type IIB supergravity and show that their Bekenstein-Hawking entropy agrees, up to a mysterious factor, with an entropy derived by counting non-BPS excitations of the Dirichlet 3-brane. These excitations are described in terms of the statistical mechanics of a 3+1 dimensional gas of massless open string states. This is essentially the classic problem of blackbody radiation. The blackbody temperature is related to the temperature of the Hawking radiation. We also construct a solution of type IIB supergravity describing a 3-brane with a finite density of longitudinal momentum. For extremal momentum-carrying 3-branes the horizon area vanishes. This is in agreement with the fact that the BPS entropy of the momentum-carrying Dirichlet 3-branes is not an extensive quantity.