Accurate calculation of gravitational wave memory

TL;DR

This paper introduces a new method based on Bondi-Metzner-Sachs theory for accurately calculating gravitational wave memory, independent of slow motion or weak field assumptions, validated with numerical relativity results.

Contribution

The authors develop a novel calculation method for gravitational wave memory that does not rely on energy flux approximations or slow motion conditions, improving accuracy.

Findings

Confirmed numerical relativity results for gravitational wave memory.

Identified dependence of memory amplitude on black hole mass ratio and spins.

Provided waveform predictions to aid memory detection and source analysis.

Abstract

Gravitational wave memory is an important prediction of general relativity. The detection of the gravitational wave memory can be used to test general relativity and to deduce the property of the gravitational wave source. Quantitative model is important for such detection and signal interpretation. Previous works on gravitational wave memory always use the energy flux of gravitational wave to calculate memory. Such relation between gravitational wave energy and memory has only been validated for post-Newtonian approximation. The result of numerical relativity about gravitational wave memory is not confident yet. Accurately calculating memory is highly demanded. Here we propose a new method to calculate the gravitational wave memory. This method is based on Bondi-Metzner-Sachs theory. Consequently our method does not need slow motion and weak field conditions for gravitational wave source. Our new method can accurately calculate memory if the non-memory waveform is known. As an example, we combine our method with matured numerical relativity result about non-memory waveform for binary black hole coalescence. We calculate the waveform for memory which can be used to aid memory detection and gravitational wave source understanding. Our calculation result confirms preliminary numerical relativity result about memory. We find out the dependence of the memory amplitude to the mass ratio and the spins of the two spin aligned black holes.