Charged rotating black holes coupled with nonlinear electrodynamics Maxwell field in the mimetic gravity

TL;DR

This paper derives new charged rotating black hole solutions in mimetic gravity with nonlinear electrodynamics, analyzing their properties, horizons, singularities, and thermodynamic stability, revealing stronger singularities and phase transitions compared to general relativity.

Contribution

It introduces novel D-dimensional charged black hole solutions with nonlinear Maxwell fields in mimetic gravity, including rotating cases and detailed thermodynamic analysis.

Findings

Black holes have at most two horizons.

Nonlinear electrodynamics causes stronger curvature singularities.

Second-order phase transition observed in thermodynamics.

Abstract

In mimetic gravity, we derive $D$-dimension charged black hole solutions having flat or cylindrical horizons with zero curvature boundary. The asymptotic behaviours of these black holes behave as (A)dS. We study both linear and nonlinear forms of the Maxwell field equations in two separate contexts. For the nonlinear case, we derive a new solution having a metric with monopole, dipole and quadrupole terms. The most interesting feature of this black hole is that its dipole and quadruple terms are related by a constant. However, the solution reduces to the linear case of the Maxwell field equations when this constant acquires a null value. Also, we apply a coordinate transformation and derive rotating black hole solutions (for both linear and nonlinear cases). We show that the nonlinear black hole has stronger curvature singularities than the corresponding known black hole solutions in general relativity. We show that the obtained solutions could have at most two horizons. We determine the critical mass of the degenerate horizon at which the two horizons coincide. We study the thermodynamical stability of the solutions. We note that the nonlinear electrodynamics contributes to process a second-order phase transition whereas the heat capacity has an infinite discontinuity.