Gravitational deflection angle of light: Definition by an observer and its application to an asymptotically nonflat spacetime. (arXiv:2001.03290v1 [gr-qc])

Gravitational deflection angle of light: Definition by an observer and its application to an asymptotically nonflat spacetime. (arXiv:2001.03290v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Takizawa_K/0/1/0/all/0/1">Keita Takizawa</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Ono_T/0/1/0/all/0/1">Toshiaki Ono</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Asada_H/0/1/0/all/0/1">Hideki Asada</a>

The gravitational deflection angle of light for an observer and source at
finite distance from a lens object has been studied by Ishihara et al. [Phys.
Rev. D, 94, 084015 (2016)], based on the Gauss-Bonnet theorem with using the
optical metric. Their approach to finite-distance cases is limited within an
asymptotically flat spacetime. By making several assumptions, we give an
interpretation of their definition from the observer’s viewpoint: The observer
assumes the direction of a hypothetical light emission at the observer position
and makes a comparison between the fiducial emission direction and the
direction along the real light ray. The angle between the two directions at the
observer location can be interpreted as the deflection angle by Ishihara et al.
The present interpretation does not require the asymptotic flatness. Motivated
by this, we avoid such asymptotic regions to discuss another integral form of
the deflection angle of light. This form makes it clear that the proposed
deflection angle can be used not only for asymptotically flat spacetimes but
also for asymptotically nonflat ones. We examine the proposed deflection angle
in two models for the latter case; Kottler (Schwarzschild-de Sitter) solution
in general relativity and a spherical solution in Weyl conformal gravity.

The gravitational deflection angle of light for an observer and source at
finite distance from a lens object has been studied by Ishihara et al. [Phys.
Rev. D, 94, 084015 (2016)], based on the Gauss-Bonnet theorem with using the
optical metric. Their approach to finite-distance cases is limited within an
asymptotically flat spacetime. By making several assumptions, we give an
interpretation of their definition from the observer’s viewpoint: The observer
assumes the direction of a hypothetical light emission at the observer position
and makes a comparison between the fiducial emission direction and the
direction along the real light ray. The angle between the two directions at the
observer location can be interpreted as the deflection angle by Ishihara et al.
The present interpretation does not require the asymptotic flatness. Motivated
by this, we avoid such asymptotic regions to discuss another integral form of
the deflection angle of light. This form makes it clear that the proposed
deflection angle can be used not only for asymptotically flat spacetimes but
also for asymptotically nonflat ones. We examine the proposed deflection angle
in two models for the latter case; Kottler (Schwarzschild-de Sitter) solution
in general relativity and a spherical solution in Weyl conformal gravity.

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