Rotating Black String with Nonlinear Source

TL;DR

This paper derives rotating black string solutions with nonlinear electromagnetic fields, analyzing their singularities, asymptotic behaviors, and thermodynamic properties, revealing how nonlinearity influences their geometric and physical characteristics.

Contribution

It introduces new rotating black string solutions with nonlinear electromagnetic sources and examines their geometric and thermodynamic properties, highlighting the effects of nonlinearity.

Findings

Born-Infeld black string has timelike singularity and anti-de Sitter asymptotics.

Power Maxwell invariant solutions' singularity type depends on nonlinearity parameter.

Conserved quantities are independent of the nonlinearity parameter.

Abstract

In this paper, we derive rotating black string solutions in the presence of two kinds of nonlinear electromagnetic fields, so called Born-Infeld and power Maxwell invariant. Investigation of the solutions show that for the Born-Infeld black string the singularity is timelike and the asymptotic behavior of the solutions are anti-deSitter, but for power Maxwell invariant solutions, depend on the values of nonlinearity parameter, the singularity may be timelike as well as spacelike and the solutions are not asymptotically anti-deSitter for all values of the nonlinearity parameter. Next, we calculate the conserved quantities of the solutions by using the counterterm method, and find that these quantities do not depend on the nonlinearity parameter. We also compute the entropy, temperature, the angular velocity, the electric charge and the electric potential of the solutions, in which the conserved and thermodynamics quantities satisfy the first law of thermodynamics.