Analytical solutions of the geodesic equation in the spacetime of a black hole in f(R) gravity

Abstract

We consider the motion of test particles in the spacetime of a black hole in f(R) gravity. The complete set of analytic solutions of the geodesic equation in the spacetime of this black hole are presented. The geodesic equations are solved in terms of Weierstrass elliptic functions and derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant $\Lambda$ and the real constant $\beta$.

28 pages, 23 figures, Accepted for publication in Physical Review D

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