A Pedagogical Model of General Covariance Coupling Electrodynamics and Gravitation

Abstract

In his 1951 model of the effects of a star’s radiation on its gravitation, P.C. Vaidya used radiation fields of flat spacetime. Wondering why Vaidya did not include the effects of gravitation on electrodynamics, we apply the principle of general covariance to gravitation and radiation. Others have addressed this problem with numerical methods, but, like Vaidya, we seek an analytic solution. Along the way, we see how prescient was Vaidya’s choice in modeling the radiation. Pursued originally as a pedagogical exercise with undergraduate physicists, our results compare favorably to similar models, and illustrate general relativity theorems. Given recent interest in teaching general relativity to undergraduates, a system that couples gravitation and electrodynamics and is solvable with elementary integrations may hold pedagogical interest.