Black holes in $f(R,T)$ gravity coupled with Euler-Heisenberg electrodynamics

TL;DR

This paper explores black hole solutions in $f(R,T)$ gravity coupled with Euler-Heisenberg nonlinear electrodynamics, analyzing their properties, horizons, and photon trajectories in various charge configurations.

Contribution

It presents new exact black hole solutions in $f(R,T)$ gravity with nonlinear electromagnetic fields, including effects of quantum corrections and effective cosmological constants.

Findings

Black hole solutions exhibit $1/r^6$ and $r^2$ correction terms.

Effective cosmological constant depends on the $f(R,T)$ coupling parameter.

Photon trajectories and stable orbits are affected by nonlinear electromagnetic effects.

Abstract

We investigate the scenario of black holes coupled with the Euler-Heisenberg nonlinear electromagnetic field in the framework of $f(R,T)$ gravity. The black hole solutions for electrically charged, magnetically charged and the dyonic case are separately analyzed, and we discuss the scalar curvature and the energy conditions of the black hole spacetime. In the magnetic charge solution, the $f(R,T)$ correction appears in the $1/r^6$ Euler-Heisenberg electromagnetic field correction term, while the electrically charged black hole solution exhibits an $r^2$ term in the metric function, corresponding to an effective cosmological constant $\Lambda_\text{eff} = \beta/(3\pi)$, inducing asymptotically anti-de Sitter or de Sitter spacetimes depending on the sign of the coupling parameter $\beta$. The dyonic solution is obtained through vacuum polarization quantum electrodynamics corrections, where electromagnetic duality is broken and the solution contains higher-order correction terms. The relationship between the event horizon and charge of dyonic extreme black holes is studied. Furthermore, we investigate the effective metric, photon trajectories, and innermost stable circular orbit under nonlinear electromagnetic effects, providing images of photon geodesic for varying electric and magnetic charge strengths and $f(R,T)$ coupling parameter.