Total light bending in non-asymptotically flat black hole spacetimes

TL;DR

This paper explores the total light bending in non-asymptotically flat black hole spacetimes using a geometric approach, revealing insights into gravitational deflection and black hole shadows in modified gravity theories.

Contribution

It revisits and applies a geometric definition of light deflection to non-asymptotically flat spacetimes, providing new analytical and numerical results.

Findings

The deflection angle is sensitive to different sources of curvature.

Near the photon sphere, the deflection angle in Horndeski gravity resembles Schwarzschild.

Black hole shadows are identical in the studied solutions.

Abstract

The gravitational deflection of light is a critical test of modified theories of gravity. A few years ago, Gibbons and Werner introduced a definition of the deflection angle based on the Gauss-Bonnet theorem. In more recent years, Arakida proposed a related idea for defining the deflection angle in non-asymptotically flat spacetimes. We revisit this idea and use it to compute the angular difference in the Kottler geometry and a non-asymptotically flat solution in Horndeski gravity. Our analytic and numerical calculations show that a triangular array of laser beams can be designed so that the proposed definition of the deflection angle is sensitive to different sources of curvature. Moreover, we find that near the photon sphere, the deflection angle in the Horndeski solution is similar to its Schwarzschild counterpart, and we confirm that the shadows seen by a static observer are identical.