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

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\"om black hole in a black hole limit and it becomes the metric of a 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 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.