Spherically symmetric charged (anti-)de Sitter black hole in $f(R,T)$ gravity coupled with nonlinear electrodynamics

TL;DR

The paper investigates static, spherically symmetric magnetically charged black holes in a gravity theory with a quadratic matter-geometry coupling $f(R,T)=R+kT^2$ intertwined with nonlinear electrodynamics described by a quadratic Lagrangian in the field invariant. An analytic BH solution is derived, yielding a metric with an effective cosmological constant $\\Lambda_{ ext{eff}} = (8/3)\\alpha(\\alpha k+\\pi)$ and high-order corrections $~r^{-6}$ and $~r^{-14}$, enriching the standard RN-AdS/dS structure and permitting multiple horizons depending on the parameters $(M,Q,\\alpha,\\gamma,k)$. The authors also treat photon propagation via an effective metric $g_{\\text{eff}}^{\\mu\\nu}$, showing that increasing magnetic charge $Q$ tends to shrink the photon sphere and shadow, while increasing the NLED parameter $\\gamma$ enlarges them, highlighting distinctive strong-field phenomenology beyond GR. Overall, the work extends $f(R,T)$ gravity with a higher-order $T^2$ coupling and nonlinear electrodynamics, revealing complex horizon configurations and observable imprint in BH shadows that could inform future astrophysical tests.

Abstract

By deriving and solving the gravitational and electromagnetic field equations in $f(R,T)$ gravity coupled with nonlinear electrodynamics, we obtain a static spherically symmetric charged solution that incorporates higher-order correction terms along with an effective cosmological constant term. This solution reduces to the AdS/dS metric in the far-field region while exhibiting significant modifications in the strong-field regime due to the nonlinear electromagnetic effects and the matter-geometry coupling. We further analyze the black hole's horizon structure, revealing the complex phenomenon of multiple horizons emerging within specific parameter ranges. Additionally, by introducing an effective metric to study photon propagation, we systematically explore the influence of magnetic charge and the coupling parameter on the effective potential, the photon sphere radius, and the black hole shadow.

Figures (6)

• Figure 1: Plot of the BH metric function $A(r)$ with parameters $Q=1$, $\alpha=-0.001$, $\gamma=0.01$ and $k=0.02$.
• Figure 2: Plot of the BH metric function $A(r)$ with parameters $M=1$, $\alpha=-0.001$, $\gamma=0.01$ and $k=0.02$.
• Figure 3: Plot of the effective potential function $V_{\mathrm{eff}}(r)$ with parameters $M=1$, $\alpha=-0.001$, $\gamma=0.06$, and $k=0.6$.
• Figure 4: Plot of the effective potential function $V_{\mathrm{eff}}(r)$ with parameters $M=1$, $Q=0.8$, $\alpha=-0.001$, and $k=0.6$.
• Figure 5: Photon geodesic structure described by the effective metric. The first row shows the relationship between the orbit number $n$ and the impact parameter $b$; the second row displays the photon geodesic curves with $M=1$, $k=0.6$, $\alpha=-0.001$ and $\gamma=0.06$.