(ed.). Gravitational waves (IOP, 2001)(422s).

Taking the scalar product we findGravitational wave radiation in the JBD theory 159c 0,0 (t) = 4π 3 S0,0 ijE ij (t)c 2,m (t) = 8π15 S2,m ijE ij (t) (11.27)and then for the NP parameters√ √51 22 =16π c 2,0(t) −4π c 0,0(t), 2 =− 1 √512 π c 2,0(t) − 1√112 π c 0,0(t)√ √1515Re 4 =−32π [c 2,2 + c 2,−2 ], Im 4 =−i32π [c 2,2 − c 2,−2 ]Re 3 = 1√1516 π [c 2,1 − c 2,−1 ], Im 3 = i√1516 π [c 2,1 + c 2,−1 ]. (11.28)Equations (11.28) relate the measurable quantities c l,m with the GW polarizationstates, described by the NP parameters. Equations (11.28) can be put incorrespondence with the output of experimental measurements if c l,m aresubstituted with their Fourier components at the quadrupole and monopoleresonant frequencies which, for the sake of simplicity, we collectively denote byω 0 . c l,m (ω 0 ) can be determined in the following way: once the Fourier amplitudesA N (ω 0 ) are measured, by Fourier transforming (11.14) and (11.15) we get theRiemann amplitudes E ij (ω 0 ) which, using (11.27), yield the desired result.In order to determine the A N (ω 0 ) amplitudes from a given GW signal thefollowing two conditions must be fulfilled:• the vibrational states of the five-fold degenerate quadrupole and monopolemodes must be determined. The quadrupole modes can be studied byproperly combining the outputs of a set of at least five motion sensorsplaced in independent positions on the sphere surface. Explicit formulas forpractical and elegant configurations of the motion sensors have been reportedby various authors [15, 16]. The vibrational state of the monopole modeis provided directly by the output of any of the above-mentioned motionsensors. If resonant motion sensors are used, since the quadrupole andmonopole states resonate at different frequencies, a sixth sensor is needed.• The spectrum of the GW signal must be sufficiently broadband to overlapwith the antenna quadrupole and monopole frequencies.11.3 Gravitational wave radiation in the JBD theoryIn this section we analyse the signal emitted by a compact binary system inthe JBD theory. We compute the scalar and tensor components of the powerradiated by the source and study the scalar waveform. Eventually we considerthe detectability of the scalar component of the radiation by interferometers andresonant-mass detectors.