Detailed study of geodesics in the Kerr-Newman-(A)dS spactime and the rotating charged black hole spacetime in $f(R)$ gravity

Abstract

We perform a detailed study of the geodesic equations in the spacetime of the static and rotating charged black hole corresponding to the Kerr-Newman-(A)dS spacetime. We derive the equations of motion for test particles and light rays and present their solutions in terms of the Weierstrass $\wp$, $\zeta$ and $\sigma$ functions as well as the Kleinian $\sigma$ function. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and classify the possible orbit types. This spacetime is also a solution of $f(R)$ gravity with a constant curvature scalar.

35 pages,3 table,24 figures, Accepted for publication in Physical Review D. arXiv admin note: text overlap with arXiv:1605.08975, arXiv:1601.03143

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• Light propagation around a Kerr-like black hole immersed in an inhomogeneous anisotropic plasma in Rastall gravity: Analytical solutions to the equations of motion
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