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

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 similar to 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 outperform the T-approximants.