Black holes and their shadows in F(R) gravity

2024/12/18 by Shin’ichi Nojiri, Sergei D. Odintsov, Nojiri, Shin'ichi +1 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Relativity and Gravitational Theory

paper · pdf · doi:10.48550/arxiv.2412.13775

Abstract

We investigate the radii of the photon sphere and the black hole shadow in the framework of F(R) gravity. For this purpose, we derive the field equation for the corresponding theory when the general spherically symmetric and static configuration is considered. This equation is the third-order differential equation with respect to F_R(r)≡ . (dF(R))/(dR)|_R=R(r), where r is the radial coordinate. Solving the equation, we find F(R) as a function of r, F_R=F_R(r). By using the assumed and obtained geometry, one can calculate the scalar curvature R as a function of r, R=R(r), which could be solved with respect to r as r=r(R). Then one finds the functional form of F_R as a function of the scalar curvature R, F_R=F_R(R)=F_R( r=r(R)).

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