Mimetic Euler-Heisenberg theory, charged solutions and multi-horizon black holes

TL;DR

This paper introduces new black hole solutions within mimetic Euler-Heisenberg gravity, analyzing their properties, thermodynamics, stability, and multi-horizon configurations, highlighting deviations from general relativity due to non-linear electrodynamics.

Contribution

It presents novel charged black hole solutions in mimetic Euler-Heisenberg theory, including multi-horizon cases, and explores their physical and thermodynamic properties.

Findings

Black holes exhibit stronger singularities than in general relativity.

Null and strong energy conditions are violated in these solutions.

Thermodynamics is consistent, but negative Hawking temperature can occur.

Abstract

We construct several new classes of black hole (BH) solutions in the context of the mimetic Euler-Heisenberg theory. We separately derive three differently charged BH solutions and their relevant mimetic forms. We show that the asymptotic form of all BH solutions behaves like a flat spacetime. These BHs, either with/without cosmological constant, have the non constant Ricci scalar, due to the contribution of the Euler-Heisenberg parameter, which means that they are not solution to standard or mimetic $f(R)$ gravitational theory without the Euler-Heisenberg non-linear electrodynamics and at the same time they are not equivalent to the solutions of the Einstein gravity with a massless scalar field. Moreover, we display that the effect of the Euler-Heisenberg theory makes the singularity of BH solutions stronger compared with that of BH solutions in general relativity. Furthermore, we show that the null and strong energy conditions of those BH solutions are violated, which is a general trend of mimetic gravitational theory. The thermodynamics of the BH solutions are satisfactory although there appears a negative Hawking temperature under some conditions. Additionally, these BHs obey the first law of thermodynamics. We also study the stability, using the geodesic deviation, and derive the stability condition analytically and graphically. Finally, for the first time and under some conditions, we derived multi-horizon BH solutions in the context of the mimetic Euler-Heisenberg theory and study their related physics.