# Gravitational memory for uniformly accelerated observers

## TL;DR

This paper explores how matter shock waves can induce a gravitational memory effect on uniformly accelerated observers in Rindler space, revealing a trajectory-dependent inhomogeneity imprint analogous to black hole supertranslational hair.

## Contribution

It demonstrates a process for implanting supertranslational hair on Rindler horizons and analyzes the resulting memory effect for accelerated observers, extending black hole memory concepts to Rindler spacetime.

## Key findings

- Observers retain a boost symmetry after the wave passes.
- The boost parameter varies with trajectory, indicating a memory effect.
- Memory encodes the inhomogeneity of the matter wave.

## Abstract

Recently, Hawking, Perry and Strominger described a physical process that implants supertranslational hair on a Schwarzschild black hole by an infalling matter shock wave without spherical symmetry. Using the BMS-type symmetries of the Rindler horizon, we present an analogous process that implants supertranslational hair on a Rindler horizon by a matter shock wave without planar symmetry, and we investigate the corresponding memory effect on the Rindler family of uniformly linearly accelerated observers. We assume each observer to remain linearly uniformly accelerated through the wave, in the sense of the curved spacetime generalisation of the Letaw-Frenet equations. Starting with a family of observers who follow the orbits of a single boost Killing vector before the wave, we find that after the wave has passed, each observer still follows the orbit of a boost Killing vector but this boost differs from trajectory to trajectory, and the trajectory-dependence carries a memory of the planar inhomogeneity of the wave. We anticipate this classical memory phenomenon to have a counterpart in Rindler space quantum field theory.