Phase transitions of black strings in dynamical Chern-Simons modified gravity

TL;DR

This paper investigates the thermodynamics and phase transitions of rotating black strings in dynamical Chern-Simons gravity, revealing a first-order phase transition and deriving key thermodynamic relations.

Contribution

It provides the first detailed analysis of black string thermodynamics in dynamical Chern-Simons gravity, including conserved charges, entropy, and phase transition behavior.

Findings

Identifies a first-order phase transition at a critical temperature.

Derives a consistent first law of thermodynamics for black strings.

Obtains a Cardy formula for the black string entropy.

Abstract

We study conserved charges and thermodynamics of analytic rotating anti-de Sitter black holes with extended horizon topology -- also known as black strings -- in dynamical Chern-Simons modified gravity. The solution is supported by a scalar field with an axionic profile that depends linearly on the coordinate that spans the string. We compute conserved charges by making use of the renormalized boundary stress-energy tensor. Then, by adopting the Noether-Wald formalism, we compute the black string entropy and obtain its area law. Indeed, the reduced Euclidean Hamiltonian approach shows that these methods yield a consistent first law of thermodynamics. Additionally, we derive a Smarr formula using a radial conservation law associated to the scale invariance of the reduced action and obtain a Cardy formula for the black string. A first-order phase transition takes place at a critical temperature between the ground state and the black string, above which the black string is the thermodynamically favored configuration.