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It is shown that gravitational waves from astronomical sources have a nonlinear effect on laser interferometer detectors on Earth, an effect which has hitherto been neglected, but which is of the same order of magnitude as the linear effects. The signature of the nonlinear effect is a permanent displacement of test masses after the passage of a wave train.PACS numbers: The need of taking full account of the nonlinearity of Einstein's equations when one wants to study the generation of gravitational waves from strong sources is generally recognized. However, since the sources are at enormous distances from the Earth, the amplitude of the waves when they reach the detector is so small that it has always been assumed that when treating the waves in the Earth's neighborhood the linearized theory suffices. It is the purpose of this Letter to show that this assumption is in error.The nonlinearity of Einstein's equations manifests itself in a permanent displacement of the test masses of a laser interferometer detector after the passage of a wave train. Such a permanent displacement, called the "memory" of the gravitational-wave burst [1,2], has long been known to occur [3] within the framework of the linearized theory as a result of an overall change of the second time derivative of the source's quadrupole moment or equivalently of an overall change of the linear momenta of the constituent bodies. As this was the only known cause of a memory effect, it was thought that typical sources, i.e., the coalescense of a neutron star binary, in which little linear momentum is radiated away, will produce bursts with negligible memory. However, we show in this Letter that every burst has a nonlinear memory, due to the cumulative contribution of the effective stress of the gravitational waves themselves. Moreover, for a binary coalescense, the nonlinear memory is of the same order of magnitude as the maximal amplitude of the dynamical part of the burst.Our treatment is based on the rigorous analysis of the asymptotic behavior of the gravitational field given in [4]. In that work we considered asymptotically flat initial data for the vacuum Einstein equations which correspond to a Cauchy hypersurface of vanishing linear momentum. We showed that if the initial data satisfy a smallness condition then they give rise to a geodesically complete spacetime. We analyzed in detail the asymptotic behavior of the solutions at null and timelike infinity. The results which have to do with the behavior at null infinity, which is what concerns us here, are largely independent of the smallness condition which was introduced to ensure completeness. Among these results is the formula for the difference of the limits Z"^ and S~ of the asymptotic shear L of outgoing null hypersurfaces C/ as u tends to + 00 and -oo^ respectively, which plays a crucial role in the present Letter. The rigorous derivation of this formula given in [4] relies heavily on the results developed in that work. For this reason we shall give below a simple derivation of the formul...

Prologue Chapter 1 : The Optical Structure Equations 1.1 The basic geometric setup 1.2 The optical structure equations 1.3 The Bianchi equations 1.4 Canonical coordinate systems Chapter 2 : The Characteristic Initial Data 2.1 The characteristic initial data 2.2 Construction of the solution in an initial domain Chapter 3 : L ∞ Estimates for the Connection Coefficients 3.1 Introduction 3.2 L ∞ estimates for χ ′ 3.3 L ∞ estimates for χ ′ 3.4 L ∞ estimates for η, η 3.5 L ∞ estimates for ω, ω 3.6 The smallness requirement on δ Chapter 4 : L 4 (S) Estimates for the 1st Derivatives of the Connection Coefficients 4.1 Introduction 4.2 L 4 (S) estimates for ∇ /χ 4.3 L 4 (S) estimates for ∇ /χ 4.4 L 4 (S) estimates for ∇ /η, ∇ /η 4.5 L 4 (S) estimates for d /ω, d /ω 4.6 L 4 (S) estimates for Dω, Dω Chapter 5 : The Uniformization Theorem 5.1 Introduction. An L 2 (S) estimate for K − K 5.2 Sobolev inequalities on S. The isoperimetric constant 5.3 The uniformization theorem 5.4 L p elliptic theory on S Chapter 6 : L 4 (S) Estimates for the 2nd Derivatives of the Connection Coefficients 6.1 Introduction 6estimate for ∇ / 2 ω 6.6 L 4 (S) estimate for ∇ / 2 ω Chapter 7 : L 2 Estimates for the 3rd Derivatives of the Connection Coefficients 7.1 Introduction 7.2 L 2 estimates for ∇ / 2 η, ∇ / 2 η 7.3 L 2 elliptic theory for generalized Hodge systems on S 7.4 L 2 estimates for ∇ / 3 χ ′ , d /K 7.5 L 2 estimates for ∇ / 3 χ ′ 7.6 L 2 estimates for ∇ / 3 η, ∇ / 3 η 7.7 L 2 estimate for ∇ / 3 ω 7.8 L 2 estimates for ∇ / 2 ω and ∇ / 3 ω 7.9 L 2 estimates for d /Dω, d /Dω, D 2 ω, D 2 ω Chapter 8 : The Multiplier Fields and the Commutation Fields 8.1 Introduction 8.2 L ∞ estimates for the deformation tensors of L, K and S 8.3 Construction of the rotation vectorfields O i 8.4 L ∞ estimates for the O i and ∇ /O i 8.5 L ∞ estimates for the deformation tensors of the O i Chapter 9 : Estimates for the Derivatives of the Deformation Tensors of the Commutation Fields 9.1 L 4 (S) estimates for the 1st derivatives of the deformation tensors of L, S 9.2 L 4 (S) estimates for the 1st derivatives of the deformation tensors of the O i 9.3 L 2 estimates for the 2nd derivatives of the deformation tensors of L, S 9.4 L 2 estimates for the 2nd derivatives of the deformation tensors of the O i Chapter 10 : The Sobolev Inequalities on the C u and C u 10.1 Introduction 10.2 The Sobolev inequalties on the C u 10.3 The Sobolev inequalities on the C u Chapter 11 : The S-tangential Derivatives and the Rotational Lie Derivatives 11.1 Introduction and preliminaries 11.2 The coercivity inequalities on the standard sphere 11.3 The coercivity inequalities on S u,u Chapter 12 : Weyl Fields and Currents. The Existence Theorem 12.1 Weyl fields and Bianchi equations. Weyl currents 12.2 Null decompositions of Weyl fields and currents 12.3 The Bel-Robinson tensor. The energy-momentum density vectorfields 12.4 The divergence theorem in spacetime 12.5 The energies and fluxes. The quantity P 2 12.6 The controlling quantity Q 2 . Bootstrap assumptions and the comparison lemma 1...

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The behaviour of the outgoing light rays in the gravitational collapse of an inhomogeneous spherically symmetric dust cloud is analyzed. It is shown that, for an open subset of initial density distributions, the first singular event, which occurs at the center of symmetry, is the vertex of an infinity of future null geodesic cones which intersect future null infinity. The frequency of the corresponding light rays is infinitely redshifted.