Gravitational bending angle of light for finite distance and the Gauss-Bonnet theorem
Gravitational bending angle of light for finite distance and the Gauss-Bonnet theorem
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DOI：
10.1103/physrevd.94.084015
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发表时间：
2016-04
影响因子：
5
通讯作者：
Asahi Ishihara;Yusuke Suzuki;T. Ono;Takao Kitamura;H. Asada
中科院分区：
文献类型：
--
作者：
Asahi Ishihara;Yusuke Suzuki;T. Ono;Takao Kitamura;H. Asada
本文讨论了静态球对称渐近平坦时空中光的弯曲角的计算到非渐近平坦时空中的一种可能的推广。本文利用光学度规研究了光的弯曲角与高斯-博内定理之间的关系。光的偏转角和高斯曲率的表面积分之间的对应关系可以使我们考虑从透镜物体到光源和接收器的有限距离。利用这个关系，我们提出了一种方法来计算这种情况下的光的弯曲角。最后，这种方法被应用到两个例子的非渐近平坦时空，建议有限距离修正：Kottler（Schwarzschild 21 {}de Sitter）的解决方案，爱因斯坦方程和精确的解决方案在Weyl共形引力。
We discuss a possible extension of calculations of the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime to a nonasymptotically flat case. We examine a relation between the bending angle of light and the Gauss-Bonnet theorem by using the optical metric. A correspondence between the deflection angle of light and the surface integral of the Gaussian curvature may allow us to take account of the finite distance from a lens object to a light source and a receiver. Using this relation, we propose a method for calculating the bending angle of light for such cases. Finally, this method is applied to two examples of the nonasymptotically flat spacetimes to suggest finite-distance corrections: the Kottler (Schwarzschild\char21{}de Sitter) solution to the Einstein equation and an exact solution in Weyl conformal gravity.