had the brilliant idea of using this firstly discovered binary pulsar system to make high-precision tests of General Relativity. Having noticed a constant shrinking of the period of revolution T , they traced it back to the emission of gravitational waves, providing the first indirect evidence for their existence. Indeed they showed that their measurements are in astonishingly precise agreement with the Einstein formula for quadrupolar gravitational radiation established in 1918. In the present chapter we plan to analyze in full detail the mechanism of gravitational radiation emission and the evidence for it provided by binary pulsar systems.

7.1.3The Coalescence of Binaries and the Interferometer Detectors

The discovery of the binary pulsar not only provided indirect evidence for gravitational waves, but also clarified the panorama of their candidate astrophysical sources. Gravitational waves are certainly emitted during the explosions of supernovae, both of type II and of type I. These events, however, are too much sporadic and the corresponding emission spectra depend on too many variables for them to be efficiently predicted. Powerful sources of gravitational radiation are also the active galactic nuclei, that are most probably occupied by giant black holes of millions of stellar masses. Stars and matter falling into such holes certainly produce gravitational waves, yet the involved wave-lengths are too large for Earth-based detectors. On the other hand, the binary pulsar provided a new paradigma of a clean, predictable and quite universal astrophysical source of gravitational radiation, whose wave-lengths are compatible with Earth-based detectors. Binary systems are quite abundant in the Universe since about fifty percent of the stars are grouped in pairs. All stars sooner or later collapse and a large fraction of them end their life as neutron stars or as black-holes. Hence binary compact star systems must be quite abundant as well. The result of Hulse and Taylor showed that such systems are instable against the slow loss of energy through gravitational radiation which, however, becomes very large and dramatic in the last few seconds before coalescence. Binary coalescences became thus the preferred astrophysical sources of gravitational radiation to be searched for. New instruments were devised and slowly constructed for the detection of such events: the gravitational interferometers.

The idea of the interferometers is just as simple as that of the resonant bars (Fig. 7.5). In this case the metric disturbance produced by the wave is supposed to deform the two arms, each a few kilometer long, of a laser interferometer, whose concept is the same as that underlying the apparatus utilized by Michelson and Morley to detect the motion of the Earth relative to the Ether. A highly monochromatic laser beam is split in two orthogonal beams that flow in the two arms of the interferometer, are reflected by mirrors placed at the arm end-points and come back, intersecting at the original splitting point. As long as the two arms are of equal length, the beams come back in phase and do not create any interference. Any gravitational