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

ContentsixPART 4Theoretical developmentsHermann Nicolai, Alessandro Nagar, Donato Bini, Fernando De Felice,Maurizio Gasperini and Luc Blanchet 24314 Infinite-dimensional symmetries in gravity 24514.1 Einstein theory 24514.1.1 Introduction 24514.1.2 Mathematical conventions 24514.1.3 The Einstein–Hilbert action 24714.1.4 Dimensional reduction D = 4 → D = 3 24714.1.5 Dimensional reduction D = 3 → D = 2 24814.2 Nonlinear σ -models 25214.2.1 Ehlers Lagrangian as a nonlinear σ -model 25414.2.2 The Ernst equation 25514.2.3 The Matzner–Misner Lagrangian as a nonlinear σ -model 25514.3 Symmetries of nonlinear σ -models 25714.3.1 Nonlinear realization of SL(2, R) E 25714.3.2 Nonlinear realization of SL(2, R) MM 25814.4 The Geroch group 25914.4.1 Action of SL(2, R) E on ˜λ, B 2 25914.4.2 Action of SL(2, R) MM on λ, B 26014.4.3 The affine Kac–Moody SL(2, R) algebra 26014.5 The linear system 26114.5.1 Solving Einstein’s equations 26114.5.2 The linear system 26314.5.3 Derivation of the colliding plane metric by factorization 265Acknowledgments 267Further reading 26715 Gyroscopes and gravitational waves 26815.1 Introduction 26815.2 Splitting formalism and test particle motion: a short review 26915.3 The spacetime metric 27215.4 Searching for an operational frame 27415.5 Precession of a gyroscope in geodesic motion 27615.6 Conclusions 278References 27816 Elementary introduction to pre-big bang cosmology and to the relicgraviton background 28016.1 Introduction 28016.2 Motivations: duality symmetry 28316.3 Kinematics: shrinking horizons 28916.4 Open problems and phenomenological consequences 294