### Abstract

The standard post-Newtonian approximation to gravitational waveforms, called T-approximants, from nonspinning black hole binaries are known not to be sufficiently accurate close to the last stable orbit of the system. A new approximation, called P-approximants, is believed to improve the accuracy of the waveforms rendering them applicable up to the last stable orbit. In this study we apply P-approximants to the case of a test particle in equatorial orbit around a Kerr black hole parameterized by a spin-parameter q that takes values between -1 and 1. In order to assess the performance of the two approximants we measure 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, that is orbits whose angular momentum is in the same sense as the spin angular momentum of the black hole, 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.

Original language | English (US) |
---|---|

Article number | 024017 |

Pages (from-to) | 024017-1-024017-20 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 71 |

Issue number | 2 |

DOIs | |

State | Published - Jan 2005 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*71*(2), 024017-1-024017-20. [024017]. https://doi.org/10.1103/PhysRevD.71.024017

}

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 71, no. 2, 024017, pp. 024017-1-024017-20. https://doi.org/10.1103/PhysRevD.71.024017

**Improved gravitational waveforms from spinning black hole binaries.** / Porter, Edward K.; Sathyaprakash, B. S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Improved gravitational waveforms from spinning black hole binaries

AU - Porter, Edward K.

AU - Sathyaprakash, B. S.

PY - 2005/1

Y1 - 2005/1

N2 - The standard post-Newtonian approximation to gravitational waveforms, called T-approximants, from nonspinning black hole binaries are known not to be sufficiently accurate close to the last stable orbit of the system. A new approximation, called P-approximants, is believed to improve the accuracy of the waveforms rendering them applicable up to the last stable orbit. In this study we apply P-approximants to the case of a test particle in equatorial orbit around a Kerr black hole parameterized by a spin-parameter q that takes values between -1 and 1. In order to assess the performance of the two approximants we measure 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, that is orbits whose angular momentum is in the same sense as the spin angular momentum of the black hole, 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.

AB - The standard post-Newtonian approximation to gravitational waveforms, called T-approximants, from nonspinning black hole binaries are known not to be sufficiently accurate close to the last stable orbit of the system. A new approximation, called P-approximants, is believed to improve the accuracy of the waveforms rendering them applicable up to the last stable orbit. In this study we apply P-approximants to the case of a test particle in equatorial orbit around a Kerr black hole parameterized by a spin-parameter q that takes values between -1 and 1. In order to assess the performance of the two approximants we measure 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, that is orbits whose angular momentum is in the same sense as the spin angular momentum of the black hole, 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.

UR - http://www.scopus.com/inward/record.url?scp=84927750910&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevD.71.024017

DO - 10.1103/PhysRevD.71.024017

M3 - Article

AN - SCOPUS:84927750910

VL - 71

SP - 024017-1-024017-20

JO - Physical Review D

JF - Physical Review D

SN - 0556-2821

IS - 2

M1 - 024017

ER -