Light Propagation and Gravitational Lensing in Weyl-Like Spacetime in Scalar-Tensor Theories of Gravity (A strophysics and Relativity)

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We study light propagation and gravitational lensing in scalar-tensor theories of gravity by using a static, axisymmetric exterior solution. This solution, which has been studied by Tsuchida and Watanabe, is asymptotically flat and, moreover, is reduced to Voorhees's solution of Weyl's series of prolate solutions in the case of a constant scalar field. We first obtain an asymptotic form of the solution near the spatial infinity in order to clarify the physical significance of three model parameters found in the solution. It is shown that an amplitude of the scalar field, the non-spherical nature of the spacetime symmetry and a masslike parameter in the Einstein frame are given in terms of these three parameters. For the spacetime structure, we give brief discussion on the anisotropic properties of the spacetime singularity. We then study null geodesic equations and Sachs's optical scalar equations on the equatorial plane in order to investigate deflection and shear of light rays. Our studies are carried out using a technique of the conformal transformation such that their results are independent of the details of the scalar-tensor theories of gravity owing to the conformally invariant properties of null geodesies. For some specific values of the model parameters, we analytically obtain a deflection angle of the light path and find that it can become negative. The appearance of a negative deflection angle indicates "reflection" of a light path, and we investigate under which conditions the light reflection occurs. As for the optical scalars, we find that the Weyl source-term exhibits the properties that differ significantly from those in the Schwarzschild spacetime. We therefore divide a space of the model parameters into four distinct regions on the basis of the qualitative properties of the Weyl source-term and find a close relationship between this classification of regions in the parameter space and the occurrence of the light reflection. We finally solve the null geodesic equations and the optical scalar equations numerically. We find that the picture of a thin lens is applicable and present a simple analytic model for optical scalars. The deflection angle and the image distortion rate of gravitational lensing are obtained as functions of the impact parameter. Again, we find a close relationship between their qualitative properties and the classification mentioned above.
理論物理学刊行会の論文
2006-03-25

Light Propagation and Gravitational Lensing in Weyl-Like Spacetime in Scalar-Tensor Theories of Gravity (A strophysics and Relativity)

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