# Persistent gravitational wave observables: general framework

## TL;DR

This paper introduces a broad framework for persistent gravitational wave observables, extending the concept of gravitational wave memory to include new measurable effects that persist after radiation passes, with practical measurement methods discussed.

## Contribution

It generalizes gravitational wave memory to a wider class of persistent effects not tied to soft theorems, providing new examples and measurement techniques.

## Key findings

- Defined a general class of persistent gravitational wave observables.
- Presented three examples including a generalized geodesic deviation, holonomy, and measurement with spinning particles.
- Discussed potential detection of these effects with current gravitational wave detectors.

## Abstract

The gravitational wave memory effect is characterized by the permanent relative displacement of a pair of initially comoving test particles that is caused by the passage of a burst of gravitational waves. Recent research on this effect has clarified the physical origin and the interpretation of this gravitational phenomenon in terms of conserved charges at null infinity and "soft theorems." In this paper, we describe a more general class of effects than the gravitational wave memory that are not necessarily associated with these charges and soft theorems, but that are, in principle, measurable. We shall refer to these effects as persistent gravitational wave observables. These observables vanish in non-radiative regions of a spacetime, and their effects "persist" after a region of spacetime which is radiating. We give three examples of such persistent observables, as well as general techniques to calculate them. These examples, for simplicity, restrict the class of non-radiative regions to those which are exactly flat. Our first example is a generalization of geodesic deviation that allows for arbitrary acceleration. The second example is a holonomy observable, which is defined in terms of a closed loop. It contains the usual "displacement" gravitational wave memory; three previously identified, though less well known memory effects (the proper time, velocity, and rotation memories); and additional new observables. Finally, the third example we give is an explicit procedure by which an observer could measure a persistent effect using a spinning test particle. We briefly discuss the ability of gravitational wave detectors (such as LIGO and Virgo) to measure these observables.