Phase structures of the black D$p$-D$(p+4)$-brane system in various ensembles I: thermal stability

TL;DR

This paper investigates the phase structures and thermal stability of black D$p$-D$(p+4)$-brane systems in various ensembles, revealing conditions for stability and phase transitions, including van der Waals-like phenomena.

Contribution

It provides a detailed analysis of the phase structures of black D$p$-D$(p+4)$-branes in different ensembles, highlighting stability conditions and the equipotency of branes.

Findings

Black branes can be stable in certain ensembles.

Van der Waals-like phase transitions occur under specific conditions.

D$(p+4)$-branes and delocalized D$p$-branes are equipotent.

Abstract

When the D$(p+4)$-brane ($p=0,1,2$) with delocalized D$p$ charges is put into equilibrium with a spherical thermal cavity, the two kinds of charges can be put into canonical or grand canonical ensemble independently by setting different conditions at the boundary. Using the thermal stability condition, we discuss the phase structures of various ensembles of this system formed in this way and find out the situations that the black brane could be the final stable phase in these ensembles. In particular, van der Waals-like phase transitions can happen when D0 and D4 charges are in different kinds of ensembles. Furthermore, our results indicate that the D$(p+4)$-branes and the delocalized D$p$-branes are equipotent.