Light curves of light rays passing through a wormhole

Gravitational lensing is a good probe into the topological structure of dark gravitating celestial objects. In this paper, we investigate the light curve of a light ray that passes through the throat of an Ellis wormhole, the simplest example of traversable wormholes. The method developed here is also applicable to other traversable wormholes. To study whether the light curve of a light ray that passes through a wormhole throat is distinguishable from that which does not, we also calculate light curves without the passage of a throat for an Ellis wormhole, a Schwarzschild black hole, and an ultrastatic wormhole with the spatial geometry identical to that of the Schwarzschild black hole in the following two cases: (i) ``microlensing, '' where the source, lens, and observer are almost aligned in this order and the light ray starts at the source, refracts in the weak gravitational field of the lens with a small deflection angle, and reaches the observer; and (ii) ``retrolensing, '' where the source, observer, and lens are almost aligned in this order, and the light ray starts at the source, refracts in the vicinity of the light sphere of the lens with a deflection angle very close to, and reaches the observer. We find that the light curve of the light ray that passes through the throat of the Ellis wormhole is clearly distinguishable from that by the microlensing but not from that by the retrolensing. This is because the light curve of a light ray that passes by a light sphere of a lens with a large deflection angle has common characters, irrespective of the details of the lens object. This implies that the light curves of the light rays that pass through the throat of more general traversable wormholes are qualitatively the same as that of the Ellis wormhole.