Global aspects of radiation memory

TL;DR

This work investigates the global structure of electromagnetic memory on a null-cone formulation, clarifying when memory can appear in the sky pattern of radiated fields. By decomposing the radiation into electric and magnetic (E/B) modes and applying a null-gauge Maxwell formulation with Hertz potentials, it proves that B-mode memory cannot arise from any physically realistic charge-current distribution, and that E-mode memory from a bound system is likewise forbidden, with memory requiring unbound or nonstationary sources. The analysis yields a memory constraint that ties the observed cumulative field change to both changes in the asymptotic Coulomb-type field and to net current flux through null infinity, and it highlights the role of ingoing radiation in possible B-mode memory. The results parallel analogous statements in gravitational memory and suggest a framework for analyzing memory effects in the coupled Einstein–Maxwell system and in astrophysical scenarios.

Abstract

Gravitational radiation has a memory effect represented by a net change in the relative positions of test particles. Both the linear and nonlinear sources proposed for this radiation memory are of the "electric" type, or E mode, as characterized by the even parity of the polarization pattern. Although "magnetic" type, or B mode, radiation memory is mathematically possible, no physically realistic source has been identified. There is an electromagnetic counterpart to radiation memory in which the velocity of charged particles obtain a net "kick". Again, the physically realistic sources of electromagnetic radiation memory that have been identified are of the electric type. In this paper, a global null cone description of the electromagnetic field is applied to establish the non-existence of B mode radiation memory and the non-existence of E mode radiation memory due to a bound charge distribution.