Bending of light and inhomogeneous Picard–Fuchs equation
【Abstract】
The bending of light rays by gravitational sources is one of the first evidence of general
relativity. When the gravitational source is a stationary massive object such as a black hole, the
bending angle has an integral representation, from which various series expansions up to a finite
order in terms of the parameters of orbit and the background spacetime has been derived. However, it
has not been 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, the full order
expansions in both weak and strong deflection limits are obtained. We show that the result can be
obtained by the direct integration approach as well. We also discuss how the charge of the
gravitational source affects...
【Author】
Tadashi Sasaki and Hisao Suzuki
【Journal】
Classical and Quantum Gravity(IF：3.5) Time：2021-06-19
