Gravitational-Wave Inspiral of Compact Binary Systems to 7/2 Post-Newtonian Order

TL;DR

This paper advances the theoretical modeling of gravitational-wave signals from compact binary inspirals by deriving 3.5PN order equations, including relativistic effects and tail contributions, crucial for gravitational wave detection.

Contribution

It provides the first derivation of the 3.5PN order equations of motion and gravitational flux for compact binaries, incorporating tail effects and relativistic corrections.

Findings

Derived 3.5PN accurate energy and flux expressions

Included tail and tail-of-tail effects in waveform modeling

Identified limitations due to point-particle regularization

Abstract

The inspiral of compact binaries, driven by gravitational-radiation reaction, is investigated through 7/2 post-Newtonian (3.5PN) order beyond the quadrupole radiation. We outline the derivation of the 3.5PN-accurate binary's center-of-mass energy and emitted gravitational flux. The analysis consistently includes the relativistic effects in the binary's equations of motion and multipole moments, as well as the contributions of tails, and tails of tails, in the wave zone. However the result is not fully determined because of some physical incompleteness, present at the 3PN order, of the model of point-particle and the associated Hadamard-type self-field regularization. The orbital phase, whose prior knowledge is crucial for searching and analyzing the inspiral signal, is computed from the standard energy balance argument.