Sources of gravitational waves in asymptotically flat Einstein-Maxwell spacetime

TL;DR

This paper develops equations describing the dynamics of isolated Einstein-Maxwell systems with gravitational and electromagnetic radiation, useful for understanding compact source evolution and black hole final states.

Contribution

It introduces a new set of equations linking gravitational and electromagnetic radiation to the system's center of mass in asymptotically flat spacetime, with comparisons to Newman’s approach.

Findings

Derived equations for low-speed regime dynamics

Identified differences with Newman’s equations on center of mass and spin

Potential applications to binary coalescence and black hole evolution

Abstract

In this work, the dynamic of isolated systems in general relativity is described when gravitational radiation and electromagnetic fields are present. In this construction, the asymptotic fields received at null infinity together with the regularized null cone cuts equation, and the center of mass of an asymptotically flat Einstein-Maxwell spacetime are used. A set of equations are derived in the low speed regime, linking their time evolution to the emitted gravitational radiation and to the Maxwell fields received at infinity. These equations should be useful when describing the dynamic of compact sources, such as the final moments of binary coalescence and the evolution of the final black hole. Additionally, we compare our equations with those coming from a similar approach given by Newman, finding some differences in the motion of the center of mass and spin of the gravitational system.