Nonlinear Gravitational Memory in the Post-Minkowskian Expansion

Area of Science:

• Gravitational Wave Physics
• General Relativity
• High-Energy Astrophysics

Background:

• The gravitational memory effect is a crucial prediction of general relativity, representing a permanent distortion of spacetime after a gravitational wave event.
• Previous calculations of the nonlinear gravitational memory waveform have been limited in scope or computational approach.

Purpose of the Study:

• To compute the leading-order nonlinear gravitational memory waveform for the scattering of two compact objects within the post-Minkowskian expansion.
• To utilize a scattering-amplitude-based approach to naturally incorporate the nonlinear memory as a soft graviton contribution.

Main Methods:

• Employing a scattering-amplitude-based representation of the gravitational waveform.
• Applying multipolar decomposition to the waveform.
• Utilizing the reverse unitarity method for exact-in-velocity predictions.

Main Results:

• The first computation of the nonlinear gravitational memory waveform for compact object scattering at leading order in the post-Minkowskian expansion.
• Explicit exact-in-velocity predictions derived from the reverse unitarity method.
• Validation of results through agreement with velocity-expanded post-Newtonian multipoles.

Conclusions:

• The study successfully computes the gauge-invariant, nonanalytic-in-frequency part of the O(G^{3}) multipolar waveform.
• The findings provide a valuable benchmark for future theoretical and observational studies of gravitational waves and compact object mergers.