Persistent gravitational wave observables: general framework (1901.00021v4)

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.

• The paper defines persistent gravitational wave observables as measurable effects in radiative spacetimes that vanish in non-radiative regions.
• It introduces systematic techniques including generalized geodesic deviation, holonomy loops, and spinning test particle methods to compute these observables.
• The study discusses potential detection with current experiments like LIGO and Virgo, providing fresh insights into spacetime curvature and gravitational dynamics.

Persistent Gravitational Wave Observables: General Framework

This paper, authored by Flanagan, Grant, Harte, and Nichols, presents a comprehensive framework for understanding a class of effects termed as "persistent gravitational wave observables." These observables extend beyond the traditional understanding of the gravitational wave memory effect, which is concerned with the permanent displacement between test particles following a burst of gravitational waves. The authors explore a broader category of effects which, although measurable, do not necessarily correlate with conserved charges or asymptotic symmetries.

Overview

The gravitational wave memory effect is a well-established phenomenon, first identified in the linearized gravitational theory and later extended to nonlinear contexts. It manifests as a measurable displacement between test masses after the passage of gravitational waves. Previous studies linked this effect to asymptotic symmetries and soft theorems, enriching our theoretical understanding of gravitational radiation.

In the present paper, the authors distinguish between traditional memory observables and a broader class of persistent observables. They introduce a systematic approach to identify and compute these effects, focusing particularly on scenarios involving transitions between non-radiative and radiative spacetime regions.

Key Contributions

1. Definition of Persistent Observables: The authors define persistent gravitational wave observables as measurements remaining nonzero in radiative spacetime regions and vanishing otherwise. Unlike traditional memory effects linked to symmetries at spacetime boundaries, these observables encapsulate broader gravitational phenomena.
2. Generalized Examples and Calculation Techniques: The paper introduces three primary examples of persistent observables:
   • Generalized Geodesic Deviation: Extending traditional geodesic deviation to account for non-comoving initial conditions and arbitrary accelerations.
   • Holonomy Observables: Defined via closed loops in spacetime, these observables encompass familiar displacement memory effects and novel ones like velocity and rotation memories.
   • Spinning Test Particle Measurements: Utilizing the Mathisson-Papapetrou equations, the authors describe procedures to measure persistent effects on spinning particles.
3. Numerical and Theoretical Implications: The paper briefly discusses the feasibility of measuring persistent observables with existing gravitational wave detectors such as LIGO and Virgo. The potential for these observables to provide insights into spacetime curvature and gravitational wave propagation is highlighted, offering fresh perspectives on gravitational wave astronomy.

Implications and Future Work

Practically, this research holds promise for enhancing gravitational wave detection capabilities, particularly in overcoming limitations inherent to traditional memory measurement techniques. Furthermore, from a theoretical standpoint, these persistent observables could elucidate aspects of spacetime dynamics not captured by memory effects alone.

As a forward-looking statement, the authors acknowledge that their current framework primarily addresses observable properties in idealized scenarios. Future studies could focus on applying this framework across a broader spectrum of spacetime configurations, including those with more complex radiative structures. Moreover, establishing a thorough connection between these persistent observables and fundamental spacetime symmetries remains an intriguing avenue for exploration.

In essence, this work not only augments our understanding of gravitational wave phenomena but also suggests novel methodologies for probing the deeper intricacies of general relativistic spacetimes.