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.
Highlights
Chern-Simons modified gravity (CSMG) is a wellknown scalar-tensor theory in four dimensions that was first proposed in Ref. [1]
We study conserved charges and thermodynamics of black strings in dynamical Chern-Simons modified gravity sourced by a scalar field with axionic profile
II we review Chern-Simons modified gravity as well as the rotating black string solutions with nontrivial scalar field obtained in Ref. [28]
Summary
Chern-Simons modified gravity (CSMG) is a wellknown scalar-tensor theory in four dimensions that was first proposed in Ref. [1]. On the other hand, constructing homogeneous black strings in GR with a nonvanishing cosmological constant is a nontrivial task due to the dynamics This issue can be circumvented by introducing scalar fields with an axionic profile, i.e., with a linear dependence on the extended flat coordinates [28,30,45]. We study conserved charges and thermodynamics of black strings in dynamical Chern-Simons modified gravity sourced by a scalar field with axionic profile To this end, we first compute conserved charges using the renormalized boundary stress-energy tensor.
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