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

Prateek Sharma,Gamal G L Nashed,Amare Abebe,Hemwati Nandan,Shobhit Giri

doi:10.3390/sym14020309

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.

Highlights

Hole Spacetime in f ( R) Gravity.The most tested theory, general relativity (GR), has proven to be the most successful in the explanation of gravity time and time again
The study of null geodesics can provide us with information about the structure of spacetime around black hole (BH) in the regime of f ( R) gravity, which is a generalizing modification to GR
This investigation may be further useful for the study of the physical properties of the BHs, given the effect of BH parameters on the trajectories of the photons passing by a BH

Summary

Introduction

All of the above are known facts that show the importance of the linear, as well as the non-linear, electrodynamics in the frame of Einstein GR and its modifications, including the f ( R) theory It is the aim of the present study to study the geodesic of the black hole presented in [40] and to discuss its physics. To obtain a corresponding BH spacetime in non-linear Maxwell f ( R) gravity, an auxiliary field Pαβ is considered to embed electromagnetism in the framework of GR (In this study, we will consider the linear case of the Maxwell equations of Equation (1) in order to make the discussion of the physics more clear, and will leave the non-linear case of the Maxwell field to a separate case in the near future).

Photon Orbit

STABILITY

Stability of Timelike Geodesics

Stability of Null Geodesics

Discussion and Conclusions