Smeared branes and the Gubser-Mitra conjecture

We argue 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 seem to provide counterexamples to the Gubser-Mitra conjecture, which links local dynamical and thermodynamic stability. By exploiting an ansatz due to Harmark and Obers, which relates charged solutions to neutral ones, we demonstrate the existence of a threshold unstable mode. This provides strong evidence for the existence of a dynamical instability, although we do not demonstrate its existence directly.

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.