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

8 Gravitational waves, theory and experiment (an overview)the matter fields is both nonlinear and non-local. The existence of such an infinitedimensionalsymmetry guarantees that the two-dimensionally reduced nonlinearfield equations are integrable. This can be shown in a standard way by exploitingthe symmetry to prove the equivalence of the theory to a system of lineardifferential equations whose compatibility conditions yield just the nonlinearequations that one wants to solve. As an example of the application of themethod to the construction of exact solutions of the two-dimensionally reducedEinstein’s equations, the results are employed to derive the exact expression ofthe metric which describe colliding plane gravitational waves with collinear andnon-collinear polarization.Gasperini’s contribution deals with string cosmology and with the basic ideasof the so-called pre-big bang scenario of string cosmology. Then it treats theinteresting problem of observable effects in different cosmological models, andin particular the so-called background of relic gravitational waves, comparing itwith the expected sensitivities of the gravitational-wave detectors. The conclusionis that the sensitivity of the future advanced detectors of gravitational waves maybe capable of detecting the background of gravitational waves predicted in thepre-big bang scenario of string cosmology and thus these detectors might testdifferent cosmological models and also string theory models.The paper by Bini and De Felice studies the problem of the behaviourof a test gyroscope on which a plane gravitational wave is impinging. Theauthors analyse whether there might be observable effects, i.e. a precession ofthe gyroscope with respect to a suitably defined frame of reference that is notFermi–Walker transported.The contribution by Luc Blanchet deals with the post-Newtoniancomputation of binary inspiral waveforms. In general relativity, the orbital phaseof compact binaries, when gravitational radiation emitted is considered, is notconstant as it is in the Newtonian calculation, but is a complex, nonlinear functionof time, depending on small post-Newtonian corrections. For the data analysison detectors, a formula containing at least the 3PN (third-post-Newtonian) orderbeyond the quadrupole formalism (see the contribution by Schutz and Ricci) isneeded, that is a formula including terms of the order of (v/c) 6 (where v isa typical velocity in the source and c is the speed of light). Blanchet’s paperthus treats the derivation of the third-post-Newtonian formula for the emission ofgravitational radiation from a self-gravitating binary system.The paper by Ed Seidel deals with numerical relativity. Among theastrophysical sources of gravitational radiation that might be detected by laserinterferometers on Earth there is the spiralling coalescence of two black holesor neutron stars. However, gravitational waves are so weak at the detectors onEarth that, as Seidel explains in his paper, one needs to know the waveform inorder to reliably detect them, in other words gravitational-wave signals can beinterpreted and detected only by comparing the observational data with a set oftheoretically determined ‘waveform templates’. Unfortunately, we can solve theEinstein’s field equations (coupled, nonlinear partial differential equations) only