Detecting gravitational waves from test-mass bodies orbiting a Kerr black hole with P-approximant templates

TL;DR

This paper compares post-Newtonian and resummed post-Newtonian templates for detecting gravitational waves from test-mass bodies orbiting Kerr black holes, finding P-approximants superior in effectualness and parameter estimation especially at high spins.

Contribution

The study demonstrates that P-approximant templates outperform T-approximants in effectualness and faithfulness for Kerr black hole signals, especially at high spins, improving gravitational wave detection and parameter estimation.

Findings

P-approximants achieve >0.99 effectualness for spins up to 0.95.

T-approximants' effectualness drops at high spins.

P-approximants have lower bias in parameter estimation.

Abstract

In this study we apply post-Newtonian (T-approximants) and resummed post-Newtonian (P-approximants) to the case of a test-particle in equatorial orbit around a Kerr black hole. We compare the two approximants by measuring their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, T-approximant templates obtain an effectualness of ~0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of > 0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q > 0. For q < 0 both T- and P-approximants perform equally well so that either of them could be used as a detection template family. However, for parameter estimation, the P-approximant templates still outperforms the T-approximants.