Black Holes and Black Strings on Cylinders

TL;DR

The paper investigates black holes on cylinders and their phase structure, focusing on the mass region where non-uniform solutions may arise. It introduces a new coordinate system and a general ansatz for non-extremal charged dilatonic branes with a transverse circle, reducing the problem to a single, charge-independent function of two variables. Thermodynamic and perturbative analyses indicate that for M > M_c there exists a non-uniform neutral black hole with horizon topology S^{d-2} × S^1 that has higher entropy than the corresponding black string, implying a quantum, non-translational instability of the uniform string. The work connects to broader themes in higher-dimensional gravity and string theory, with implications for stability, phase transitions, and holographic contexts such as little string theory and AdS/CFT.

Abstract

We review the recently discovered ansatz that describes non-extremal charged dilatonic branes of string/M-theory with a transverse circle. The ansatz involves a new coordinate system that interpolates between the spherical and cylindrical case, and reduces the equations of motion to a set of equations on one unknown function of two variables. The function is independent of the charge, so that the ansatz can also be used to construct neutral black holes on cylinders and near-extremal charged dilatonic branes with a transverse circle. The construction enables us to argue that, for sufficiently large mass, there exists a neutral solution that breaks translational invariance in the circle direction, and has larger entropy than that of the neutral black string of the same mass.