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

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.

Scalarization of Chern-Simons Kerr Black Hole Solutions and Wormholes

“…Allowing the axion field to be dynamical a solution describing a rotating black hole in the small coupling slow rotation limit was found in [12]. Static and rotating black string solutions in dynamical CS modified gravity were studied in [13,14].…”

Bianchi IX geometry and the Einstein–Maxwell theory

“…The exact solutions for the metric function H(r, x) in D-dimensional Einstein-Maxwell theory with an embedded four-dimensional Eguchi-Hanson type II geometry (6.18) in the spatial section of the spacetime, is given by [24] (6.20) where ξ 6+2n = π 2 (2n + 1)! !, n = 0, 1, 2, .…”

“…The black hole solutions with different type of topologies for the horizon also were constructed and explored in [23]. Moreover, the references [24,25] include the other solutions to extended theories of gravity with different type of matter fields in different dimensions. The class of solutions to Einstein-Maxwell-dilaton theory, in which the dilaton field couples to the cosmological constant and the Maxwell field, was considered in [26].…”