Abstract
For the last decade, the gravitational lensing in the strong gravitational field has been studied eagerly. It is well known that, for the lensing by a black hole, infinite number of Einstein rings are formed by the light rays which wind around the black hole nearly on the photon sphere, which are called relativistic Einstein rings. This is also the case for the lensing by a wormhole. In this paper, we study the Einstein ring and relativistic Einstein rings for the Schwarzschild black hole and the Ellis wormhole, the latter of which is an example of traversable wormholes of the Morris-Thorne class. Given the configuration of the gravitational lensing and the radii of the Einstein ring and relativistic Einstein rings, we can distinguish between a black hole and a wormhole in principle. We conclude that we can detect the relativistic Einstein rings by wormholes which have the radii of the throat $a\simeq 0.5$pc at a galactic center with the distance 10Mpc and which have $a\simeq 10$AU in our galaxy using by the most powerful modern instruments which have the resolution of $10^{-2}$arcsecond such as a 10-meter optical-infrared telescope. The black holes which make the Einstein rings of the same size as the ones by the wormholes are galactic supermassive black holes and the relativistic Einstein rings by the black holes are too small to measure at this moment. We may test some hypotheses of astrophysical wormholes by using the Einstein ring and relativistic Einstein rings in the future.
Highlights
Gravitational lensing is a very useful tool for astrophysics and cosmology
Frittelli et al [8], Virbhadra and Ellis [9, 10] and Bozza et al [11] studied the gravitational lensing in the strong field with the Schwarzschild spacetime and found the infinite Einstein rings which are too close to each other to separately resolve
The gravitational lensing in the strong field on the spherically symmetric static spacetime was investigated by Bozza [12], Hasse and Perlick [13] and Perlick [14]
Summary
Gravitational lensing is a very useful tool for astrophysics and cosmology. At first the gravitational lensing mainly was investigated on a theoretical basis in the weak gravitational field. Frittelli et al [8], Virbhadra and Ellis [9, 10] and Bozza et al [11] studied the gravitational lensing in the strong field with the Schwarzschild spacetime and found the infinite Einstein rings which are too close to each other to separately resolve. The gravitational lensing in the strong field on the spherically symmetric static spacetime was investigated by Bozza [12], Hasse and Perlick [13] and Perlick [14] They showed that the relativistic Einstein rings are formed in the Schwarzschild spacetime and in the other spherically symmetric static spacetime. We will consider the Einstein ring and relativistic Einstein rings in the Ellis spacetime and the Schwarzschild spacetime, both of which are static and spherically symmetric ones.
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