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

TL;DR

This paper analytically solves null geodesics in a hyperbolic topological black hole spacetime within conformal Weyl gravity, deriving exact horizon expressions and photon deflection angles without approximations.

Contribution

It provides the first exact solutions for photon paths and horizon locations in this specific black hole spacetime, using elliptic functions and without approximations.

Findings

Exact null geodesic solutions using elliptic functions

Analytical expressions for black hole horizons

Photon deflection angles derived without approximation

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.