On the Null Trajectories in Conformal Weyl Gravity

TL;DR

This paper derives exact null geodesic solutions around black holes in conformal Weyl gravity, including horizon expressions, motion analysis, and photon deflection angles without approximations, highlighting differences from general relativity.

Contribution

It provides the first exact analytical solutions for photon trajectories and deflection angles in conformal Weyl gravity, expanding understanding of light behavior in this alternative gravity theory.

Findings

Exact horizon expressions depend on cosmological and coupling constants.

Photon deflection angles are obtained analytically without approximations.

Null geodesics are characterized using elliptic functions in this gravity model.

Abstract

In this work we find analytical solutions to the null geodesics around a black hole in the conformal Weyl gravity. Exact expressions for the horizons are found, and they depend on the cosmological constant and the coupling constants of the conformal Weyl gravity. Then, we study the radial motion from the point of view of the proper and coordinate frames, and compare it with that found in spacetimes of general relativity. The angular motion is also examined qualitatively by means of an effective potential; quantitatively, the equation of motion is solved in terms of $\wp$-Weierstrass elliptic function. Thus, we find the deflection angle for photons without using any approximation, which is a novel result for this kind of gravity.