A gravitational memory effect in "boosted" black hole perturbation theory

TL;DR

This paper explores the impact of non-zero ADM momentum on black hole perturbation theory, revealing a novel gravitational memory effect distinct from the Christodoulou effect.

Contribution

It introduces the consideration of non-vanishing ADM momentum in black hole perturbation theory and identifies a new gravitational memory effect.

Findings

Transformation to the center of momentum frame affects gravitational wave amplitude.

A new gravitational memory effect is identified, unrelated to the Christodoulou effect.

The study provides a theoretical basis for including ADM momentum in perturbation analyses.

Abstract

Black hole perturbation theory, or more generally, perturbation theory on a Schwarzschild bockground, has been applied in several contexts, but usually under the simplifying assumption that the ADM momentum vanishes, namely, that the evolution is carried out and observed in the ``center of momentum frame''. In this paper we consider some consequences of the inclusion of a non vanishing ADM momentum in the initial data. We first provide a justification for the validity of the transformation of the initial data to the ``center of momentum frame'', and then analyze the effect of this transformation on the gravitational wave amplitude. The most significant result is the possibility of a type of gravitational memory effect that appears to have no simple relation with the well known Christodoulou effect.