G. I. Róis, J. T. S. S. Junior, F. S. N. Lobo, M. E. Rodrigues, T. Harko
Abstract
In this work, we investigate static and spherically symmetric black hole solutions in f(R,T) gravity, where R is the curvature scalar and T is the trace of the energy-momentum tensor, coupled to nonlinear electrodynamics (NLED). To construct our solutions, we adopt a linear functional form, f(R,T)=R+βT. In the limit β=0, the theory reduces to general relativity, recovering f(R,T)≈R. We propose a power-law Lagrangian of the form L=f0+F+αFp, where α=f0=0 corresponds to the linear electrodynamics case. Using this setup, we derive the metric functions and determine an effective cosmological constant. Our analysis focuses on specific cases with p=2, p=4, and p=6, where we formulate analytic expressions for the matter fields supporting these solutions in terms of the Lagrangian as a function of F. Additionally, we verify the regularity of the solutions and study the structure of the event horizons. Furthermore, we examine a more specific scenario by determining the free forms of the first and second derivatives LF(r) and LFF(r) of the Lagrangian of the nonlinear electromagnetic field. From these relations, we derive the general form of LNLED(r) using consistency relations. This Lagrangian exhibits an intrinsic nonlinearity due to the influence of two constants, α and β. Specifically, α originates from the power-law term in the proposed Lagrangian, while β arises from the assumed linear function f(R,T). The interplay of these constants ensures that the nonlinearity of the Lagrangian is governed by both α and β, rather than α alone. By imposing specific constraints, namely, setting α=0 and β=0, the model reduces to the linear electrodynamics case, while still remaining consistent with the f(R,T) gravity framework. This demonstrates the model's flexibility in describing both linear and nonlinear regimes.
Keywords
General relativity / alternative theories of gravity / General Relativity and Quantum Cosmology / High Energy Astrophysical Phenomena / High Energy Physics - Theory
Physical Review D
Volume 111, Issue 124044, Page 17
2025 June
