Memory effects from holonomies

TL;DR

This paper unifies electromagnetic and gravitational memory effects using a gravito-electromagnetic framework, revealing novel relativistic corrections, radial effects, and a holonomy-based formulation on holographic screens in asymptotically flat spacetimes.

Contribution

It introduces a unified approach to memory effects, derives new relativistic corrections, and formulates these effects in terms of holonomies on holographic screens.

Findings

Relativistic corrections to displacement and kick memory in gauge theory and GR.

Discovery of novel radial memory effects in both theories.

Holonomy formulations relate memory effects to Wilson loops and Lorentz parts.

Abstract

We provide a uniform treatment of electromagnetic and gravitational memory effects, based on the gravito-electromagnetic formulation of GR and a generalization of the geodesic deviation equation. This allows us to find novel results: in gauge theory, we derive relativistic corrections to the well-known kick memory observable, and a general expression for the displacement memory observable, typically overlooked in the literature. In GR, we find relativistic corrections to displacement and kick memory observables. In both theories, we find novel radial memory effects. Next, we show that electromagnetic and gravitational memory observables can be formulated in terms of certain holonomies on a holographic screen in asymptotically flat spacetimes. In gauge theory, the displacement and kick memory effects form a Hamiltonian vector field which is canonically generated by a Wilson loop. In the first order formulation of GR, we show that the holonomy naturally splits into translational and Lorentz parts. While the former encodes the leading and subleading displacement and kick memory observables, the latter reproduces the gyroscopic memory effect.