Smeared branes and the Gubser-Mitra conjecture

TL;DR

The paper addresses the link between dynamical GL instability and local thermodynamic stability (GM conjecture) for smeared branes, showing that a GL-type instability can exist along the smeared direction even when the specific heat condition $C_Q>0$ holds, thereby countering GM. It leverages the Harmark-Obers ansatz to relate charged smeared branes to neutral solutions, demonstrating that a threshold unstable mode at a finite wavelength, set by $R_0$, persists for all charges and can vanish near extremality as $R_0\to 0$ with $M$ fixed. This reveals that smeared charged branes can be dynamically unstable despite local thermodynamic stability, challenging the generality of GM-type criteria. The results motivate a refined view of stability for higher-dimensional branes and suggest deeper connections to the end-states of GL-type instabilities and dual field theory descriptions.

Abstract

We show that smeared brane solutions, where a charged black p-brane is smeared uniformly over one of the transverse directions, can have a Gregory-Laflamme type dynamical instability in the smeared direction even when the solution is locally thermodynamically stable. These thus provide counterexamples to the Gubser-Mitra conjecture, which links local dynamical and thermodynamic stability. The existence of a dynamical instability is demonstrated by exploiting an ansatz due to Harmark and Obers, which relates charged solutions to neutral ones.

Figures (2)

• Figure 1: Phase diagram for neutral solutions for a five-dimensional system on a circle.
• Figure 2: The bold lines now refer to charged solutions. The diagram is qualitatively the same as in the neutral situation, shown as dotted lines for reference.