Photon paths in the hyperbolic topological black hole spacetime of conformal Weyl gravity

Abstract

In this work we find analytical solutions to the null geodesics in the hyperbolic topological black hole spacetime of conformal Weyl gravity in an invariant $2$-plane given by the orbits of an azimuthal Killing vector. Exact expressions for the (non-compact) horizons are found, which depend on the cosmological constant and the coupling constants of conformal Weyl gravity. The angular motion is examined qualitatively by means of an effective potential; quantitatively, the equation of motion is solved in terms of the $\wp$-Weierstra{\ss} elliptic function. Thus, we find the deflection angle for photons without using any approximation, which is a novel result for this topology.