On the null trajectories in conformal Weyl gravity

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 ℘-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.

Null paths on a toroidal topological black hole in conformal Weyl gravity

“…Finally, our study provides a simple physical visualization of the null trajectories and their main issues, and complements other studies carried out in the standard and/or trivial topology [15,49].…”

Classical tests on a charged Weyl black hole: bending of light, Shapiro delay and Sagnac effect

“…Thus, an observer at r = r i essentially observes the same behavior for photons crossing either of the horizons in a similar manner as that in the spherically symmetric spacetimes in the context of general relativity [28,29]. Same holds for uncharged Weyl black holes [23] (see Fig. 2).…”

“…This final solution satisfies the vacuum field equations of the 4th order conformal Weyl gravity (CWG). The theory was therefore proposed as an alternative to the dark matter/dark energy scenario [9], and it has been studied from several points of view [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. May or may not being the proper alternative theory to Einstein gravity, the Weyl gravity however exhibits interesting properties.…”

Light bending, static dark energy, and related uniqueness of Schwarzschild–de Sitter spacetime

“…[23]- [29] for discussions on light bending in de Sitter black hole spacetimes with rotation and charge. In [30,31,32], discussions of this phenomenon in the context of conformal and some other modified gravity theories can be found. See [33] for a discussion on the effect of a naked curvature singularity on light bending.…”