Deriving Weak Deflection Angle by Black Holes or Wormholes using Gauss-Bonnet Theorem

TL;DR

This review discusses methods based on the Gauss-Bonnet theorem for calculating light deflection angles caused by black holes and wormholes, including effects of plasma and finite-distance corrections, in various spacetime models.

Contribution

It comprehensively reviews the Gibbons-Werner method and alternative approaches for weak gravitational lensing by black holes and wormholes, highlighting new applications and corrections.

Findings

Gauss-Bonnet theorem effectively computes deflection angles.

Finite-distance and plasma effects significantly influence light bending.

Jacobi metric yields consistent results with traditional methods.

Abstract

In this review, various researches on finding the bending angle of light deflected by a massive gravitating object which regard the Gauss-Bonnet theorem as the premise have been revised. Primarily, the Gibbons and Werner method is studied apropos of the gravitational lensing phenomenon in the weak field limits. Some exclusive instances are deliberated while calculating the deflection angle, beginning with the finite-distance corrections on non-asymptotically flat spacetimes. Effects of plasma medium is then inspected to observe its contribution to the deflection angle. Finally, the Jacobi metric is explored as an alternative method, only to arrive at similar results. All of the cases are probed in three constructs, one as a generic statement of explanation, one for black holes, and one for wormholes, so as to gain a perspective on every kind of influence.