Modeling a circular equatorial test-particle in a Kerr spacetime

TL;DR

This paper improves the accuracy of gravitational wave flux models for circular equatorial orbits in Kerr spacetime by extending re-summation techniques, including absorption effects, to enhance waveform templates for EMRI detection.

Contribution

It introduces an improved flux approximation method using inverted Chebyshev polynomials, incorporating absorption effects, and extends the flux model to 5.5PN order for Kerr black holes.

Findings

Absorption effects improve flux model convergence.

Inverted Chebyshev approximation outperforms other re-summation methods.

Extended flux model to 5.5PN order for Kerr spacetime.

Abstract

Extreme Mass Ratio Inspirals (EMRIs) are one of the main gravitational wave (GW) sources for a future space detector, such as eLISA/NGO, and third generation ground-based detectors, like the Einstein Telescope. These systems present an interest both in astrophysics and fundamental physics. In order to make a high precision determination of their physical parameters, we need very accurate theoretical waveform models or templates. In the case of a circular equatorial orbit, the key stumbling block to the creation of these templates is the flux function of the GW. This function can be modeled either via very expensive numerical simulations, which then make the templates unusable for GW astronomy, or via some analytic approximation method such as a post-Newtonian approximation. This approximation is known to be asymptotically divergent and is only known up to 5.5PN order for the Schwarzschild case and to 4PN order for the Kerr case. A way to improve the convergence of the flux is to use re-summation methods. In this work we extend previous results using the Pad\'e and Chebyshev approximations, first by taking into account the absorption of the GWs by the central black hole which was neglected in previous studies, and secondly by using the information from the Schwarzschild and absorption terms to create a Kerr flux up to 5.5PN order. We found that these two additions both improve the convergence. We also demonstrate that the best re-summation method for improving the flux model is based on a flux function which we call the "inverted Chebyshev approximation".