LG (Landau-Ginzburg) in GL (Gregory-Laflamme)

TL;DR

This paper introduces a Landau-Ginzburg thermodynamic approach to analyze the Gregory-Laflamme instability of black strings, generalizes the analysis to torus compactifications, and explores the phase structure and transition order.

Contribution

It presents a novel Landau-Ginzburg based method for studying black string instabilities and extends the analysis to arbitrary torus compactifications.

Findings

The critical dimension cannot be lowered by torus compactification.

Transition order depends only on the number of extended dimensions.

Richer phase structures emerge in torus compactifications.

Abstract

This paper continues the study of the Gregory-Laflamme instability of black strings, or more precisely of the order of the transition, being either first or second order, and the critical dimension which separates the two cases. First, we describe a novel method based on the Landau-Ginzburg perspective for the thermodynamics that somewhat improves the existing techniques. Second, we generalize the computation from a circle compactification to an arbitrary torus compactifications. We explain that the critical dimension cannot be lowered in this way, and moreover in all cases studied the transition order depends only on the number of extended dimensions. We discuss the richer phase structure that appears in the torus case.