Geodesics of a Static Charged Black Hole Spacetime in f(R) Gravity

Abstract

In recent years, the modification of general relativity (GR) through f(R) gravity is widely used to study gravity in a variety of scenarios. In this article, we study various physical properties of a black hole (BH) that emerged in the linear Maxwell f(R) gravity to constrain the values of different BH parameters, i.e., c and α. In particular, we study those values of the defining α and c for which the particles around the above-mentioned BH behave like other astrophysical BH in GR. The main motivation of the present research is to study the geodesics equations and discuss the possible orbits for c=0.5 in detail. Furthermore, the frequency shift of a photon emitted by a timelike particle orbiting around the BH is studied given different values of α and c. The stability of both timelike and null geodesics is discussed via Lyapunov’s exponent.

Trajectory of massive particles around a static black hole in f(R) gravity

“…It is clear to us from (24) that PNP diverges at event horizon, then reaches maximum point at r = r max where f (r max ) = 0 and it will decreases at larger distance from r max . This clearly indicates that the gravitational field due to this PNP will be repulsive for distance larger than r max .…”

“…The study on thermal corrections and phase transition for static black hole in f (R) gravity was made in [23]. Prateek Sharma and others [24] have studied the geodesics of a static charged black hole in f (R) gravity. A brief study on static and spherically symmetric black holes in f (R) gravity theories can be found in [25].…”

“…Gravitational potential will be zero for static radius (r s ), so f (r s ) = 1 in (24). Hence the circular orbit of massive particles can have the radius r c in the following range [28]:…”

“…where ψ is the PNP calculated in (24) and l stands for pseudo-Newtonian angular momentum per particle mass. Circular orbits (Keplerian) can be obtained when dv eff dr = 0 and as a result we get…”

Trajectory of Massive Particles around a Static Black Hole in f(R) Gravity

“…The study on thermal corrections and phase transition for static black hole in f(R) gravity was made in [22]. Prateek Sharma an others [23] have studied the geodesics of a Static Charged black hole in f(R) gravity. A brief study on static and spherically symmetric black holes in f(R) gravity theories can be found [24].…”