Memories of Gravitational Shockwaves

TL;DR

This work analyzes how plane-fronted gravitational shockwaves imprint memory on classical scalar and electromagnetic fields and on test-particle trajectories. Using a sandwich-type GSW with a metric characterized by $H(v,u,y)=\chi(u) f(v,y)$, it shows that memory depends on the spatial profile $f(y)$ and manifests as a near-front coordinate transformation generated by the vector $\zeta$ implementing Penrose supertranslations, i.e., $\phi_0={\cal L}_\zeta \bar{\phi}$ and $\delta u^\mu={\cal L}_\zeta \bar{u}^\mu$ at the shock. The analysis derives perturbation equations for scalar fields and Maxwell fields in this background, revealing that memory effects are captured by Lie-derivative transformations and, for EM fields, by a transition-radiation term with $l_\mu \hat{F}^{\mu\nu} \simeq \bar{\chi}(u) (l_\mu {\cal L}_\zeta \bar{F}^{\mu\nu} - {\cal J}^\nu)$. The results unify particle, scalar, and EM memory under a geometric framework and suggest observable signatures near magnetars and in fast radio bursts, while also connecting to the physics of null cosmic strings.

Abstract

Gravitational shockwaves produce perturbations of field systems. We study classical scalar and electromagnetic fields and gravitational memory effects left after the action on the fields of plane-fronted gravitational shockwaves. The gravitational memory plays a key role for the choice of Cauchy data which determine the perturbations. We demonstrate that field systems`remember' only a spatial `profile' of the shock, but not the form of the signal. Moreover the dependence on the spatial profile can be expressed in a geometric way as a transformation of fields under coordinate supertranslations defined near the shockwave front. We also discuss applications of our results to astrophysics.