New Black Hole Solution in f(R) Theory and Its Related Physics - G. G. L. Nashed; Ali Eid (Universe)
Recent observations suggest that General Relativity (GR) faces challenges in fully explaining phenomena in regimes of strong gravitational fields. A promising alternative is the <semantics>f(R)</semantics> theory of gravity, where R denotes the Ricci scalar. This modified theory aims to address the limitations observed in standard GR. In this study, we derive a black hole (BH) solution without introducing nonlinear electromagnetic fields or imposing specific constraints on R or the functional form of <semantics>f(R)</semantics> gravity. The BH solution obtained here is different from the classical Schwarzschild solution in GR and, under certain conditions, reduces to the Schwarzschild (A)dS solution. This BH is characterized by the gravitational mass of the system and an additional parameter, which distinguishes it from GR BHs, particularly in the asymptotic regime. We show that the curvature invariants of this solution remain well defined at both small and large values of r. Furthermore, we analyze their thermodynamic properties, demonstrating consistency with established principles such as Hawking radiation, entropy, and quasi-local energy. This analysis supports their viability as alternative models to classical GR BHs.