The Response of Test Masses to Gravitational Waves in the Coordinates of a Local Observer

A Theresponseoflaserinterferom etersto gravitationalwaveshasbeen calculated in a num berofdi(cid:11)erentways,particularly in the transverse-tracelessand the local Lorentz gauges. At (cid:12)rst sight, it would appear that these calculations lead to di(cid:11)erentresultswhen theseparation between thetestm assesbecom escom parableto thewavelength ofthegravitationalwave.In thispaperthisdiscrepancy isresolved. W e describe the response offree test m asses to plane gravitationalwaves in the coordinate fram e ofa localobserver and show that it acquires contributions from three di(cid:11)erent e(cid:11)ects: the displacem ent ofthe test m asses,the apparent change in the photon velocity,and the variation in the clock speed ofthe localobserver, allofwhich are induced by the gravitationalwave. O nly when taken together do these three e(cid:11)ects represent a quantity which is translationally invariant. This translationally-invariantquantity isidenticalto the response function calculated in thetransverse-tracelessgauge.W ethusresolvethewell-known discrepancy between thetwocoordinatessystem s,and show thattheresultsfound in thecoordinatefram e ofa localobserverare valid forlarge separation between the m asses.

[1]  F.Ya.Khalili.  Frequency-dependent rigidity in large-scale interferometric gravitational-wave detectors , 2001, gr-qc/0107084.

[2]  A. Buonanno,et al.  Quantum noise in second generation, signal recycled laser interferometric gravitational wave detectors , 2001, gr-qc/0102012.

[3]  M. Rakhmanov.  Dynamics of laser interferometric gravitational wave detectors , 2000 .

[4]  B. Barish,et al.  LIGO and the Detection of Gravitational Waves , 1999 .

[5]  Frequency response of Michelson- and Sagnac-based interferometers , 1997 .

[6]  P. Saulson.  Fundamentals of Interferometric Gravitational Wave Detectors , 1994 .

[7]  A. Ortolan,et al.  Light phase shift in the field of a gravitational wave , 1991 .

[8]  A. Ortolan,et al.  Some remarks on electromagnetic detectors of gravitational waves. , 1990 .

[9]  Marco Lops,et al.  The VIRGO Project: A wide band antenna for gravitational wave detection , 1990 .

[10]  P. Fortini,et al.  On the crucial role played by the reference system in gravitational-wave detector theory , 1987 .

[11]  J. Vinet.  Erratum - Recycling interferometric antennas for periodic gravitational waves , 1986 .

[12]  M. Orlandini,et al.  Comparison between the Fermi normal and the transverse traceless co-ordinate system , 1986 .

[13]  F. Estabrook.  Response functions of free mass gravitational wave antennas , 1985 .

[14]  P. Fortini,et al.  Fermi normal co-ordinate system and electromagnetic detectors of gravitational waves , 1982 .

[15]  L. Grishchuk,et al.  GRAVITATIONAL WAVES AND THEIR INTERACTION WITH MATTER AND FIELDS , 1980 .

[16]  F. Pegoraro,et al.  On the operation of a tunable electromagnetic detector for gravitational waves , 1978 .

[17]  L. Grishchuk.  REVIEWS OF TOPICAL PROBLEMS: Gravitational waves in the cosmos and the laboratory , 1977 .

[18]  Hugo D. Wahlquist,et al.  Response of Doppler spacecraft tracking to gravitational radiation , 1975 .

[19]  In Gravitation: an introduction to current research , 1962 .

[20]  R. Lindsay,et al.  General relativity and gravitational waves , 1962 .

[21]  J. Synge,et al.  Relativity: The General Theory , 1960 .

[22]  A. Peres.  Some Gravitational Waves , 1959 .

[23]  F. Pirani,et al.  Gravitational waves in general relativity III. Exact plane waves , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[24]  E. M. Lifshitz,et al.  Classical theory of fields , 1952 .