Abstract
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 * .
Highlights
In 1919, the experimental confirmation of the theory of general relativity [1] succeeded [2]
We study the geodesic curvature of the photon orbit on the equatorial plane in the stationary and axisymmetric spacetime by using the generalized optical metric
We provided a brief review of a series of works on the deflection angle of light for a light source and receiver in a non-asymptotic region. [38,39,42,43]
Summary
In 1919, the experimental confirmation of the theory of general relativity [1] succeeded [2]. Ishihara et al have successfully extended Gibbons and Werner’s idea such that the source and receiver can be at a finite distance from the lens object [38]. We hope that the detailed calculations in this paper will be helpful for readers to compute the gravitational deflection of light by the new powerful method This new technique has been used to study the gravitational lensing in rotating Teo wormholes [43] and in Damour–Solodukhin wormholes [44].
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