Gravitational lensing by a Bronnikov-Kim wormhole under a weak-field approximation and in a strong deflection limit

TL;DR

This paper analyzes gravitational lensing by a Bronnikov-Kim wormhole under weak and strong gravitational fields, revealing identical deflection angle coefficients in both limits and providing exact calculations without parameter expansion.

Contribution

It provides the first exact expressions for deflection angles in both weak and strong limits for a Bronnikov-Kim wormhole, linking black hole and wormhole geometries.

Findings

Deflection angle coefficients are identical in both limits.

Exact expressions for deflection angles are obtained without parameter expansion.

The metric transitions smoothly between black hole and wormhole geometries.

Abstract

We consider gravitational lensing under a weak-field approximation and in a strong deflection limit by a Bronnikov-Kim wormhole with the same metric as the one of a wormhole which has been suggested in Einstein-Dirac-Maxwell theory. The metric approaches into the metric of an extreme charged Reissner-Nordstr\"{o}m black hole in a black hole limit and it becomes the metric of an spatial Schwarzschild wormhole in an ultrastatic limit. In both of the black hole limit and the ultrastatic limit, the coefficient of a divergent term and the constant term of the deflection angle of a light in the strong deflection limit can be obtained exactly without expanding of parameters of the spacetime. Interestingly, in the both limits to the black hole and the ultrastatic wormhole, we obtain exactly the same coefficient and constant term in the strong deflection limit.