Thermodynamics and Stability of Flat Anti-de Sitter Black Strings

TL;DR

This paper investigates the thermodynamic stability and phase transitions of 5D flat AdS black strings, revealing their stability and the conditions under which phase transitions occur with AdS soliton backgrounds.

Contribution

It provides a detailed analysis of phase transitions and stability of flat AdS black strings, confirming the Gubser-Mitra conjecture for these spacetimes.

Findings

Flat AdS black strings are thermodynamically stable with always positive specific heat.

A phase transition exists between flat AdS black strings and AdS soliton strings.

Both configurations are free of Gregory-Laflamme instability across all mass parameters.

Abstract

We examine the thermodynamics and stability of 5-dimensional flat anti-de Sitter (AdS) black strings, locally asymptotically anti-de Sitter spacetimes whose spatial sections are AdS black holes with Ricci flat horizons. We find that there is a phase transition for the flat AdS black string when the AdS soliton string is chosen as the thermal background. We find that this bulk phase transition corresponds to a 4-dimensional flat AdS black hole to AdS soliton phase transition on the boundary Karch-Randall branes. We compute the possibility of a phase transition from a flat AdS black string to a 5-dimensional AdS soliton and show that, though possible for certain thin black strings, the transition to the AdS soliton string is preferred. In contrast to the case of the Schwarzschild-AdS black string, we find that the specific heat of the flat AdS black string is always positive; hence it is thermodynamically stable. We show numerically that both the flat AdS black string and AdS soliton string are free of a Gregory-Laflamme instability for all values of the mass parameter. Therefore the Gubser-Mitra conjecture holds for these spacetimes.