Black Hole Solution Free of Ghosts in f(R) Gravity Coupled with Two Scalar Fields

Abstract

One extension of general relativity, known as f(R) gravity, where R denotes the Ricci scalar, is regarded as a promising candidate for addressing the anomalies observed in conventional general relativity. In this work, we apply the field equations of f(R) gravity to a spacetime with spherical symmetry with distinct metric potentials, i.e., gtt≠grr. By solving the resulting nonlinear differential equations, we derive a novel black hole solution without imposing constraints on the Ricci scalar or on the specific form of f(R) gravity. This solution does not reduce to the Schwarzschild solution of Einstein’s general relativity. This solution is notable because it includes a gravitational mass and extra terms that make the singularities in the curvature stronger than those in black holes from Einstein’s general relativity. We analyze these black holes within the framework of thermodynamics and demonstrate their consistency with standard thermodynamic quantities. Furthermore, we investigate the stability by examining odd-type perturbation modes and show that the resulting black hole is stable. Finally, we derive the coefficients of the two scalar fields and demonstrate that the black hole obtained in this study is free from ghosts.