Journal
UNIVERSE
Volume 5, Issue 11, Pages -Publisher
MDPI
DOI: 10.3390/universe5110218
Keywords
gravitational lens; general relativity; black hole; wormhole
Funding
- JSPS
- Japan Society for the Promotion of Science [18J14865, 17K05431]
- Ministry of Education, Culture, Sports, Science, and Technology [17H06359]
- Grants-in-Aid for Scientific Research [18J14865, 17K05431] Funding Source: KAKEN
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In order to clarify the effects of the finite distance from a lens object to a light source and a receiver, the gravitational deflection of light has been recently reexamined by using the Gauss-Bonnet (GB) theorem in differential geometry (Ishihara et al. 2016). The purpose of the present paper is to give a short review of a series of works initiated by the above paper. First, we provide the definition of the gravitational deflection angle of light for the finite-distance source and receiver in a static, spherically symmetric and asymptotically flat spacetime. We discuss the geometrical invariance of the definition by using the GB theorem. The present definition is used to discuss finite-distance effects on the light deflection in Schwarzschild spacetime for both the cases of weak deflection and strong deflection. Next, we extend the definition to stationary and axisymmetric spacetimes. We compute finite-distance effects on the deflection angle of light for Kerr black holes and rotating Teo wormholes. Our results are consistent with the previous works if we take the infinite-distance limit. We briefly mention also the finite-distance effects on the light deflection by Sagittarius A*.
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