Characteristics of Gravitational and Electromagnetic Radiation

Both gravitational and electromagnetic radiation travel along light rays, which are principal null directions in space-time. They are characteristic surfaces of Einstein and Maxwell equations. We start with the coupled Einstein-Maxwell equations together with the Maxwell equations, for a space-time given by the null Bondi-Sachs line element, and a null electromagnetic gauge field. In this characteristic framework, we deduce analytical expressions describing the gravitational waves and the electromagnetic counterparts at infinity, as well as the nonlinear effects of the interaction between them, such as radiation memory. The source of gravitational and electromagnetic radiation is treated as a black box, and therefore the approach is very flexible, with potentially large applicability.