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Register a new userGravitational deflection angle of light: Definition by an observer and its application to an asymptotically nonflat spacetime
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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 observers 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. Effects of finite distance on the light deflection in Weyl conformal gravity result in an extra term in the deflection angle, which may be marginally observable in a certain parameter region. On the other hand, those in Kottler spacetime are beyond reach of the current technology.
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By using a method improved with a generalized optical metric, the deflection of light for an observer and source at finite distance from a lens object in a stationary, axisymmetric and asymptotically flat spacetime has been recently discussed [Ono, Ishihara, Asada, Phys. Rev. D 96, 104037 (2017)]. By using this method, in the weak field approximation, we study the deflection angle of light for an observer and source at finite distance from a rotating Teo wormhole, especially by taking account of the contribution from the geodesic curvature of the light ray in a space associated with the generalized optical metric. Our result of the deflection angle of light is compared with a recent work on the same wormhole but limited within the asymptotic source and observer [Jusufi, Ovgun, Phys. Rev. D 97, 024042, (2018)], in which they employ another approach proposed by Werner with using the Nazims osculating Riemannian construction method via the Randers-Finsler metric. We show that the two different methods give the same result in the asymptotic limit. We obtain also the corrections to the deflection angle due to the finite distance from the rotating wormhole.
By using a method improved with a generalized optical metric, the deflection of light for an observer and source at finite distance from a lens object in a stationary, axisymmetric and asymptotically flat spacetime has been recently discussed [Ono, Ishihara, Asada, Phys. Rev. D {bf 96}, 104037 (2017)]. In this paper, we study a possible extension of this method to an asymptotically nonflat spacetime. We discuss a rotating global monopole. Our result of the deflection angle of light is compared with a recent work on the same spacetime but limited within the asymptotic source and observer [Jusufi et al., Phys. Rev. D {bf 95}, 104012 (2017)], in which they employ another approach proposed by Werner with using the Nazims osculating Riemannian construction method via the Randers-Finsler metric. We show that the two different methods give the same result in the asymptotically far limit. We obtain also the corrections to the deflection angle due to the finite distance from the rotating global monopole. Near-future observations of Sgr A${}^{*}$ will be able to put a bound on the global monopole parameter $beta$ as $1- beta < 10^{-3}$ for a rotating global monopole model, which is interpreted as the bound on the deficit angle $delta < 8times 10^{-4}$ [rad].
Continuing work initiated in an earlier publication [Ishihara, Suzuki, Ono, Kitamura, Asada, Phys. Rev. D {bf 94}, 084015 (2016) ], we discuss a method of calculating the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime, especially by taking account of the finite distance from a lens object to a light source and a receiver. For this purpose, we use the Gauss-Bonnet theorem to define the bending angle of light, such that the definition can be valid also in the strong deflection limit. Finally, this method is applied to Schwarzschild spacetime in order to discuss also possible observational implications. The proposed corrections for Sgr A$^{ast}$ for instance are able to amount to $sim 10^{-5}$ arcseconds for some parameter range, which may be within the capability of near-future astronomy, while also the correction for the Sun in the weak field limit is $sim 10^{-5}$ arcseconds.
We calculate the exact solutions to the equations of motion that govern the light ray trajectories as they travel in a Kerr black holes exterior that is considered to be filled with an inhomogeneous and anisotropic plasmic medium. This is approached by characterizing the plasma through conceiving a radial and an angular structure function, which are let to be constant. The description of the motion is carried out by using the Hamilton-Jacobi method, that allows defining two effective potentials, characterizing the evolution of the polar coordinates. The elliptic integrals of motion are then solved analytically, and the evolution of coordinates is expressed in terms of the Mino time. This way, the three-dimensional demonstrations of the light ray trajectories are given respectively.
In order to clarify 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 cases of the 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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