Transformation of the multipolar components of gravitational radiation under rotations and boosts

TL;DR

This paper analyzes how gravitational wave multipolar components transform under rotations and boosts, emphasizing the importance of frame choice for accurate waveform modeling in black hole mergers.

Contribution

It introduces a formalism for transforming gravitational radiation multipoles under rotations and boosts, aiding in waveform analysis and simulation accuracy.

Findings

Rotations simplify waveforms in the remnant black hole's frame.

Boosts are crucial for accurate gravitational-wave phasing.

Frame choice significantly impacts numerical simulation results.

Abstract

We study the transformation of multipolar decompositions of gravitational radiation under rotations and boosts. Rotations to the remnant black hole's frame simplify the waveforms from the merger of generic spinning black hole binaries. Boosts may be important to get an accurate gravitational-wave phasing, especially for configurations leading to large recoil velocities of the remnant. As a test of our formalism we revisit the classic problem of point particles falling into a Schwarzschild black hole. Then we highlight by specific examples the importance of choosing the right frame in numerical simulations of unequal-mass, spinning binary black-hole mergers.