A gravitational wave propagating in the direction is usually described by the transverse spatial components , , in the transverse traceless gauge in which . The transverse components are not changed by a gauge transformation, which implies that the traceless condition must be automatically met. We analyze how this comes about in the calculation of the waves in an explicit example, a circular binary orbit of equal mass points. This calculation is a useful exercise in linearized general relativity and gravitational waves, and a model of an important astrophysical source of detectable waves. We also demonstrate automatic transverse tracelessness for the general case of a slow motion source.
REFERENCES
1.
R.
Vogt
, “The U.S. LIGO Project
” in Sixth Marcel Grossman Meeting on General Relativity (Proceedings, Kyoto, Japan, 1991)
, edited by H.
Sato
and T.
Nakamura
(World Scientific
, Singapore, 1992
), pp. 244
–266
.2.
B.
Abbott
et al. (LSC), “Detector description and performance for the first coincidence observations between LIGO and GEO
,” Nucl. Instrum. Methods Phys. Res. A
A517
, 154
–179
(2004
);B.
Abbott
et al., “Upper limits on gravitational wave bursts in LIGO’s second science run
,” Phys. Rev. D
72
, 062001
–1
(2005
).3.
K.
Danzmann
and A.
Rudiger
, “LISA technology-concept, status, prospects
,” Class. Quantum Grav.
20
, S1
–S10
(2003
).4.
For a discussion of gauge invariance in linearized theory see
D.
Garfinkle
, “Gauge invariance and the detection of gravitational radiation
,” Am. J. Phys.
74
, 196
–199
(2006
).5.
C. W.
Misner
, K. S.
Thorne
, and J. A.
Wheeler
, Gravitation
(Freeman
, San Francisco, 1973
).6.
Reference 5, Sec. 18.1.
7.
Reference 5, Eq. (18.14).
8.
Reference 5, Eq. (36.43).
9.
J.
Mathews
and R. L.
Walker
, Mathematical Methods of Physics
(Benjamin
, Menlo Park, 1970
), 2nd ed., Sec. 9.5.© 2008 American Association of Physics Teachers.
2008
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.