Classical and Thermodynamic Stability of Black Branes

TL;DR

The paper explores the relationship between classical Gregory-Laflamme instability and thermodynamic stability in black branes, showing that instability disappears near extremality for certain branes but persists for others, with implications for supergravity solutions.

Contribution

It establishes a link between classical and thermodynamic stability of black branes and analyzes the conditions under which Gregory-Laflamme instability vanishes near extremality.

Findings

Instability correlates with thermodynamic instability in black branes.

For p=1,2,4, the Gregory-Laflamme instability disappears near extremality.

For p=5,6, the instability persists down to extremality.

Abstract

It is argued that many non-extremal black branes exhibit a classical Gregory-Laflamme instability if, and only if, they are locally thermodynamically unstable. For some black branes, the Gregory-Laflamme instability must therefore disappear near extremality. For the black $p$-branes of the type II supergravity theories, the Gregory-Laflamme instability disappears near extremality for $p=1,2,4$ but persists all the way down to extremality for $p=5,6$ (the black D3-brane is not covered by the analysis of this paper). This implies that the instability also vanishes for the near-extremal black M2 and M5-brane solutions.