论文标题
光和不均匀的Picard-fuchs方程的弯曲
Bending of Light and Inhomogeneous Picard-Fuchs Equation
论文作者
论文摘要
引力源弯曲光线是总体相对性的第一个证据之一。当重力souce是一个固定的巨大物体（例如黑洞）时，弯曲角具有积分表示，从轨道参数和背景时空的参数方面，各种串联膨胀得出。但是，尚不清楚它具有任何分析性扩展。在本文中，我们表明，可以通过解决不均匀的Picard-fuchs方程来获得Schwarzschild黑洞的情况，该方程已应用于Calabi-Yau歧管中的D-Branes上的有效超电势。从弯曲角的分析表达中，明确获得了弱和强挠度扩展。我们证明结果可以通过直接集成方法获得。我们还讨论了重力源的电荷如何影响弯曲角，并表明可以为极端reissner-Nordstrom时空获得类似的分析表达。
Bending of light rays by gravitational sources is one of the first evidences of the general relativity. When the gravitational souce is a stationary massive object such as a black hole, the bending angle has an integral representation, from which various series expansions in terms of the parameters of orbit and the background spacetime has been derived. However, it is not clear that it has any analytic expansion. In this paper, we show that such an analytic expansion can be obtained for the case of a Schwarzschild black hole by solving an inhomogeneous Picard-Fuchs equation, which has been applied to compute effective superpotentials on D-branes in the Calabi-Yau manifolds. From the analytic expression of the bending angle, both weak and strong deflection expansions are explicitly obtained. We show that the result can be obtained by the direct integration approach. We also discuss how the charge of the gravitational source affects the bending angle and show that a similar analytic expression can be obtained for the extremal Reissner-Nordstroem spacetime.
