Post-adiabatic dynamics and waveform generation in self-force theory: an invariant pseudo-Hamiltonian framework

TL;DR

This paper introduces a gauge-invariant, pseudo-Hamiltonian framework for 1PA gravitational waveform modeling in self-force theory, avoiding direct self-force calculations and clarifying conserved quantities.

Contribution

It develops a gauge-invariant 1PA waveform-generation method using a pseudo-Hamiltonian approach on phase space, incorporating conservation laws and localizing dynamics.

Findings

A gauge-invariant 1PA waveform framework is established.

The pseudo-Hamiltonian structure naturally defines conserved quantities.

The conservative Hamiltonian matches the first law of binary black hole mechanics.

Abstract

Gravitational waveform modeling in self-force theory has reached a mature stage in recent years, with fast and accurate models emerging at both adiabatic (0PA) and first post-adiabatic (1PA) orders in a multiscale expansion. Here, we provide a gauge-invariant 1PA waveform-generation framework that involves no direct calculation of the (gauge-dependent) self-force. To achieve this, we recast the multiscale framework in a pseudo-Hamiltonian form, working on the six-dimensional phase space intrinsic to the multiscale expansion. We characterize the gauge freedom on phase space and show how a localization procedure avoids nonlocal-in time effects in the 1PA dynamics. We find a conservative Hamiltonian structure can be naturally embedded into the complete, dissipative 1PA pseudo-Hamiltonian dynamics, giving rise to natural definitions of the conserved energy, angular momentum, and radial and polar actions. As a byproduct, we clarify that the on-shell value of the conservative Hamiltonian is equal to the mechanical energy historically predicted by the first law of binary black hole mechanics.