Gravitational radiation for extreme mass ratio inspirals to the 14th post-Newtonian order

TL;DR

This paper derives high-order gravitational waveforms up to 14th post-Newtonian order for extreme mass ratio inspirals, improving waveform accuracy for gravitational wave detection and data analysis.

Contribution

The authors compute the 14PN order energy flux for circular orbits around Schwarzschild black holes and propose a fitting formula for higher order coefficients applicable to Kerr black holes.

Findings

Phase difference of 10^-7 after two years inspiral at 14PN order.

14PN waveforms achieve accuracy comparable to numerical waveforms for LISA.

Convergence analysis of the PN expansion and a method to extract higher order coefficients.

Abstract

We derive gravitational waveforms needed to compute the 14th post-Newtonian (14PN) order energy flux for a particle in circular orbit around a Schwarzschild black hole, i.e. $v^{28}$ beyond the leading Newtonian approximation where $v$ is the orbital velocity of a test particle. We investigate the convergence of the energy flux in the PN expansion and suggest a fitting formula which can be used to extract unknown higher order PN coefficients from accurate numerical data for more general orbits around a Kerr black hole. The phase difference between the 14PN waveforms and numerical waveforms after two years inspiral is shown to be about $10^{-7}$ for $\mu/M=10^{-4}$ and $10^{-3}$ for $\mu/M=10^{-5}$ where $\mu$ is the mass of a compact object and $M$ the mass of the central supermassive black hole. In first order black hole perturbation theory, for extreme mass ratio inspirals which are one of the main targets of Laser Interferometer Space Antenna, the 14PN expressions will lead to the data analysis accuracies comparable to the ones resulting from high precision numerical waveforms.