Gravitational waves by a particle in circular orbits around a Schwarzschild black hole: 5.5 postNewtonian formula

Using the post-Newtonian (PN) expansion technique of the gravitational wave perturbation around a Schwarzschild black hole, we calculate analytically the energy flux of gravitational waves induced by a particle in circular orbits up to the 5.5PN order, i.e.

O(v~{11})

beyond Newtonian. By comparing the formula with numerical data, we find that the error of the 5.5PN formula is about 4% when the particle is on the last stable circular orbit. We also estimate the error

\Delta N

in the total cycle of gravitational waves from coalescing compact binaries in a laser interferometer's band produced by using the post-Newtonian approximations. We find that, as for the neutron star-black hole binaries, the 4.5PN approximation gives \Delta N\alt1 for a black hole of mass

M<40M_\odot

, while it gives \Delta N\agt1 for a black hole of mass

M>40M_{\odot}

.

Note:

Revised

gravitational radiation: induced
energy: flux
black hole: Schwarzschild
black hole: orbit
n: matter
luminosity
interference: laser
numerical calculations

References(13)

Figures(0)

The Last three minutes: issues in gravitational wave measurements of coalescing compact binaries

Curt Cutler
(
- Caltech
)
,
Theocharis A. Apostolatos
(
- Caltech
)
,
Lars Bildsten
(
- Caltech
)
,
Lee Samuel Finn
(
- Northwestern U.
)
,
Eanna E. Flanagan
(
- Caltech
)

et al.

- Phys.Rev.Lett. 70 (1993) 2984-2987
•
e-Print:
- astro-ph/9208005
•
DOI:
- 10.1103/PhysRevLett.70.2984

- Phys.Rev.Lett. 74 L3515

PostNewtonian expansion of gravitational waves from a particle in circular orbit around a Schwarzschild black hole

Hideyuki Tagoshi
(
- Kyoto U.
)
,
Misao Sasaki
(
- Kyoto U.
)

- Prog.Theor.Phys. 92 (1994) 745-772
•
e-Print:
- gr-qc/9405062
•
DOI:
- 10.1143/PTP.92.745

Gravitational radiation from a particle in circular orbit around a black hole. 1: Analytical results for the nonrotating case

Eric Poisson
(
- Caltech
)

- Phys.Rev.D 47 (1993) 1497-1510
•
DOI:
- 10.1103/PhysRevD.47.1497

Gravitational radiation from a particle in circular orbit around a black hole. 4: Analytical results for the slowly rotating case

Eric Poisson
(
- Caltech
)

- Phys.Rev.D 48 (1993) 1860-1863
•
DOI:
- 10.1103/PhysRevD.48.1860

Gravitational waves from a point particle in circular orbit around a black hole: Logarithmic terms in the postNewtonian expansion

- Phys.Rev.D 49 (1994) 4016-4022
•
DOI:
- 10.1103/PhysRevD.49.4016

PostNewtonian expansion of the ingoing wave Regge-Wheeler function

Misao Sasaki
(
- Kyoto U.
)

- Prog.Theor.Phys. 92 (1994) 17-36,
- Prog. Theor. Phys. 92 (1994) 17-36, and Kyoto U. - KUNS-1246 (94/02,rec.Mar.) 31 p
•
e-Print:
- gr-qc/9402042
•
DOI:
- 10.1143/PTP.92.17

Analytic solutions of the Teukolsky equation and their low frequency expansions

Shuhei Mano
(
- Osaka U. and
- Hokkaido U.
)
,
Hisao Suzuki
(
- Osaka U. and
- Hokkaido U.
)
,
Eiichi Takasugi
(
- Osaka U. and
- Hokkaido U.
)

- Prog.Theor.Phys. 95 (1996) 1079-1096
•
e-Print:
- gr-qc/9603020
•
DOI:
- 10.1143/PTP.95.1079

Tidal interactions of inspiraling compact binaries

- Astrophys.J. 400 (1992) 175-180
•
DOI:
- 10.1086/171983

Gravitational radiation from a particle in circular orbit around a black hole. 6. Accuracy of the postNewtonian expansion

Eric Poisson
(
- Washington U., St. Louis
)

- Phys.Rev.D 52 (1995) 5719-5723,
- Phys.Rev.D 55 (1997) 7980-7981 (addendum)
•
e-Print:
- gr-qc/9505030
•
DOI:
- 10.1103/PhysRevD.52.5719

Gravitational radiation from a particle in circular orbit around a black hole. 2: Numerical results for the nonrotating case

- Phys.Rev.D 47 (1993) 1511-1518
•
DOI:
- 10.1103/PhysRevD.47.1511

Gravitational waves from a particle orbiting around a rotating black hole: PostNewtonian expansion

- Phys.Rev.D 51 (1995) 1646-1663
•
e-Print:
- gr-qc/9409054
•
DOI:
- 10.1103/PhysRevD.51.1646

PostNewtonian expansion of gravitational waves from a particle in circular orbits around a rotating black hole: Up to O (v**8) beyond the quadrupole formula

Hideyuki Tagoshi
(
- Caltech and
- Natl. Astron. Observ. of Japan
)
,
Masaru Shibata
(
- Caltech and
- Natl. Astron. Observ. of Japan
)
,
Takahiro Tanaka
(
- Osaka U.
)
,
Misao Sasaki
(
- Osaka U.
)

- Phys.Rev.D 54 (1996) 1439-1459
•
e-Print:
- gr-qc/9603028
•
DOI:
- 10.1103/PhysRevD.54.1439