Static and rotating black strings in dynamical Chern-Simons modified gravity

TL;DR

This paper constructs static and rotating black string solutions in dynamical Chern-Simons gravity, exploring their properties with and without torsion, and analyzing how scalar fields and topological invariants influence the solutions.

Contribution

It presents new black string solutions in dynamical Chern-Simons gravity with detailed analysis of torsion and scalar field couplings, extending previous models.

Findings

Solutions are locally AdS3 × R and extend BTZ black holes.

Nonminimal scalar couplings generate torsion in vacuum.

Torsion affects the effective cosmological constant.

Abstract

Four-dimensional homogeneous static and rotating black strings in dynamical Chern-Simons modified gravity, with and without torsion, are presented. Each solution is supported by a scalar field that depends linearly on the coordinate that span the string. The solutions are locally $\mbox{AdS}_3 \times \mathbb{R}$ and they represent the continuation of the Ba\~nados-Teitelboim-Zanelli black hole. Moreover, they belong to the so-called Chern-Simons sector of the space of solutions of the theory, since the Cotton tensor contributes nontrivially to the field equations. The case with nonvanishing torsion is studied within the first-order formalism of gravity, and it considers nonminimal couplings of the scalar fields to three topological invariants: Nieh-Yan, Pontryagin and Gauss-Bonnet terms, which are studied separately. These nonminimal couplings generate torsion in vacuum, in contrast to Einstein-Cartan theory. In all cases, torsion contributes to an effective cosmological constant that, in particular cases, can be set to zero by a proper choice of the parameters.