Using analogies with electromagnetic radiation, we present a calculation of the properties of gravitational radiation emitted by orbiting binary objects. The calculation produces results that have the same dependence on the masses of the orbiting objects, the orbital frequency, and the mass separation as do the results from the linear version of general relativity (GR). However, the calculation yields polarization, angular distributions, and overall power results that differ from those of GR. Nevertheless, the calculation produces waveforms that are very similar to those observed by the Laser Interferometer Gravitational-Wave Observatory (LIGO-VIRGO) gravitational wave collaboration in 2015 up to the point at which the binary merger occurs. The details of the calculation should be understandable by upper-level physics students and physicists who are not experts in GR.
References
1.
B. P.
Abbott
et al., “Observation of gravitational waves from a binary black hole merger
,” Phys. Rev. Lett.
116
, 061102
(2016
).2.
B. P.
Abbott
et al., “GW151226: Observation of gravitational waves from a 22-solar-mass binary black hole coalescence
,” Phys. Rev. Lett.
116
, 241103
(2016
).3.
Don
Lincoln
and Amber
Stuver
, “Ripples in reality
,” Phys. Teach.
54
, 398
–403
(2016
).4.
B. P.
Abbott
et al., “GW170104: Observation of a 50-solar-mass binary black hole coalescence at redshift 0.2
,” Phys. Rev. Lett.
118
, 221101
(2017
).5.
LIGO Scientific
and VIRGO Collaborations
, “The basic physics of the binary black hole merger GW150914
,” Ann. Phys.
529
, 1600209
(2017
).6.
Daniel
Kennefick
, “Controversies in the history of the radiation reaction problem in general relativity
,” e-print arXiv:gr-qc/97040021-33 (1997
).7.
Daniel
Kennefick
, Traveling at the Speed of Thought: Einstein and the Quest for Gravitational Waves
(Princeton U.P.
, Princeton
, 2007
).8.
Hans
Ohanian
and Remo
Ruffini
, Gravitation and Spacetime
, 2nd ed. (W. W. Norton & Company
, New York
, 1994
).9.
Abraham
Pais
, Subtle is the Lord: The Science and the Life of Albert Einstein
(Oxford U.P.
, New York
, 1982
).10.
Bernard F.
Schutz
, “Gravitational waves on the back of an envelope
,” Am. J. Phys.
52
, 412
–419
(1984
).11.
12.
13.
Thomas A.
Moore
, A General Relativity Workbook
(University Science Books
, Mill Valley, California
, 2013
).14.
David J.
Griffiths
, Introduction to Electrodynamics
, 4th ed. (Pearson-Addison-Wesley
, New York
, 2012
).15.
J. D.
Jackson
, Classical Electrodynamics
, 2nd ed. (John Wiley & Sons
, New York
, 1975
).16.
J. D.
Jackson
and L. B.
Okun
, “Historical roots of gauge invariance
,” Rev. Mod. Phys.
73
, 663
–680
(2001
).19.
O. L.
Brill
and B.
Goodman
, “Causality in the Coulomb gauge
,” Am. J. Phys.
35
, 832
–837
(1967
).20.
P. C.
Peters
, “Where is the energy stored in a gravitational field?
,” Am. J. Phys.
49
, 564
–569
(1981
).21.
Reference 7 describes the history of this argument originally developed by Bondi and Pirani. The most famous version is due to Feynman and is called the “sticky bead argument.” <https://en.wikipedia.org/wiki/Sticky_bead_argument>.
22.
Using the term Schwarzschild radius violates our pre-1915 scenario since Schwarzschild did not publish his solution of Einsein's equation for static, spherically symmetric mass distributions until 1916.
23.
Colin
Montgomery
, Wayne
Orchiston
, and Ian
Whittingham
, “Michell, Laplace, and the origin of the black hole concept
,” J. Astron. Hist. Herit.
12
, 90
–96
(2009
).24.
A video simulation of two black holes merging can be found at <https://apod.nasa.gov/apod/ap160212.html>.
25.
26.
Peter R.
Saulson
, “If light waves are stretched by gravitational waves, how can we use light as a ruler to detect gravitational waves?
,” Am. J. Phys.
65
, 501
–505
(1997
).27.
Robert L.
Forward
, “Wideband laser-interferometer gravitational-radiation experiment
,” Phys. Rev. D
17
, 379
–390
(1978
).28.
Atsushi
Nishizawa
, Atsushi
Taruya
, Kazuhiro
Hayama
, Seiji
Kawamura
, and Masa-aki
Sakagami
, “Probing non-tensorial polarization of stochastic gravitational-wave backgrounds with ground-based laser interferometers
,” Phys. Rev. D
79
, 082002
(2009
).29.
Maximiliano
Isi
, Alan J.
Weinstein
, Carver
Mead
, and Matthew
Pitkin
, “Detecting beyond-Einstein polarizations of continuous gravitational waves
,” Phys. Rev. D
91
, 082002
(2015
).30.
Louis J.
Rubbo
, Shane L.
Larson
, Michelle B.
Larson
, and Dale R.
Ingram
, “Hands-on gravitational wave astronomy: Extracting astrophysical information from simulated signals
,” Am. J. Phys.
75
, 597
–601
(2007
).31.
J.
Amato
, Physics From Planet Earth: Gravitational Radiation 2; available at <https://physicsfromplanetearth.wordpress.com/2016/05/> Accessed August 29, 2017
.32.
John G.
Baker
, Joan
Centrella
, Dae-Il
Choi
, Michael
Koppitz
, and James
van Meter
, “Gravitational-wave extraction from an inspiralling configuration of merging black holes
,” Phys. Rev. Lett.
96
, 111102
(2006
).33.
Thibault
Damour
, Frontiers in Relativistic Celestial Mechanics, Theory
, Sergei M.
Kopeikin
, editor (de Gruyter
, Berlin, 2014
) Vol. 1, pp. 1
–38
.34.
The LIGO Open Science Center
URL is <https://losc.ligo.org/>.35.
B. P.
Abbott
et al., “Properties of the binary black hole merger GW150914
,” Phys. Rev. Lett.
116
, 241102
(2016
).36.
Richard H.
Price
, “General relativity primer
,” Am. J. Phys.
50
, 300
–329
(1982
).37.
B. P.
Abbot
et al., “GW170814: A three-detector observation of gravitational waves from a binary black hole coalescence
,” Phys. Rev. Lett.
119
, 141101
(2017
).38.
B. P.
Abbott
et al.. “GW170817: Observation of gravitational waves from a binary neutron star inspiral
,” Phys. Rev. Lett.
119
, 161101
(2017
).39.
J. M.
Weisberg
, D. J.
Nice
, and J. H.
Taylor
, “Timing measurements of the relativistic binary pulsar PSR B1913+16
,” Astrophys. J.
722
, 1030
–1034
(2010
).40.
Adrian
Cho
, “The cosmos aquiver
,” Science
354
, 1516
–1517
(2017
).© 2018 American Association of Physics Teachers.
2018
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