記述言語：英語   掲載種別：研究論文（学術雑誌）  

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 mass-like 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.

DOI： 10.1143/PTP.115.487

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Yukawa Institute for Theoretical Physics  

We study series of stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent to the exterior solutions in some class of scalar-tensor theories of gravity. First, we classify spherical exterior solutions into two types of solutions, an apparently black hole type solution and an apparently worm hole type solution. The solutions contain three parameters, and we clarify their physical significance. Second, we reduce the field equations for the axisymmetric exterior solutions. We find that the reduced equations are partially the same as the Ernst equations. As simple examples, we derive new series of static, axisymmetric exterior solutions, which correspond to Voorhees's solutions. We then establish a non-trivial relation between the spherical exterior solutions and our new solutions. Finally, since null geodesies have conformally invariant properties, we study the local geometry of the exterior solutions by using the optical scalar equations and find some anomalous behavior of the null geodesics.

DOI： 10.1143/PTP.101.73

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Yukawa Institute for Theoretical Physics  

We derive a modified Buchdahl inequality for scalar-tensor theories of gravity. In general relativity, Buchdahl has shown that the maximum value of the mass-to-size ratio, 2M/R, is 8/9 for static and spherically symmetric stars under some physically reasonable assumptions. We formally apply Buchdahl's method to scalar-tensor theories and obtain theory-independent inequalities. After discussing the mass definition in scalar-tensor theories, these inequalities are related to a theory-dependent maximum mass-to-size ratio. We show that its value can exceed not only Buchdahl's limit, 8/9, but also unity, which we call the black hole limit, in contrast to general relativity. Next, we numerically examine the validity of the assumptions made in deriving the inequalities and the applicability of our analytic results. We find that the assumptions are mostly satisfied and that the mass-to-size ratio exceeds both Buchdahl's limit and the black hole limit. However, we also find that this ratio never exceeds Buchdahl's limit when we impose the further condition, ρ - 3p ≥ 0, on the density, ρ, and pressure, p, of the matter.

DOI： 10.1143/PTP.100.291

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：EDP Sciences  

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