Author | Klainerman, Sergiu. author |
---|---|
Title | The Evolution Problem in General Relativity [electronic resource] / by Sergiu Klainerman, Francesco Nicolรฒ |
Imprint | Boston, MA : Birkhรคuser Boston, 2003 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2084-8 |
Descript | 400 p. online resource |
1 Introduction -- 1.1 Generalities about Lorentz manifolds -- 1.2 The Einstein equations -- 1.3 Local existence for Einsteinโs vacuum equations -- 1.4 Appendix -- 2 Analytic Methods in the Study of the Initial Value Problem -- 2.1 Local and global existence for systems of nonlinear wave equations -- 2.2 Weyl fields and Bianchi equations in Minkowski spacetime -- 2.3 Global nonlinear stability of Minkowski spacetime -- 2.4 Structure of the work -- 3 Definitions and Results -- 3.1 Connection coefficients -- 3.2 Bianchi equations in an Einstein vacuum spacetime -- 3.3 Canonical double null foliation of the spacetime -- 3.4 Deformation tensors -- 3.5 The definitions of the fundamental norms -- 3.6 The initial data -- 3.7 The Main Theorem -- 4 Estimates for the Connection Coefficients -- 4.1 Preliminary results -- 4.2 Proof of Theorem Ml -- 4.3 Proof of Theorem 4.2.1 and estimates for the zero and first derivatives of the connection coefficents -- 4.4 Proof of Theorem 4.2.2 and estimates for the second derivatives of the connection coefficients -- 4.5 Proof of Theorem 4.2.3 and control of third derivatives of the connection coefficients -- 4.6 Rotation tensor estimates -- 4.7 Proof of Theorem M2 and estimates for the D norms of the rotation deformation tensors -- 4.8 Appendix -- 5 Estimates for the Riemann Curvature Tensor -- 5.1 Preliminary tools -- 5.2 Appendix -- 6 The Error Estimates -- 6.1 Definitions and prerequisites -- 6.3 The error terms ?2 -- 6.4 Appendix -- 7 The Initial Hypersurface and the Last Slice -- 7.1 Initial hypersurface foliations -- 7.2 The initial hypersurface connection estimates -- 7.3 The last slice foliation -- 7.4 The last slice connection estimates -- 7.5 The last slice rotation deformation estimates -- 7.6 The extension argument -- 7.7 Appendix -- 8 Conclusions -- 8.1 The spacetime null infinity -- 8.2 The behavior of the curvature tensor at the null-outgoing infinity -- 8.3 The behavior of the connection coefficients at the null-outgoing infinity. -- 8.4 The null-outgoing infinity limit of the structure equations -- 8.5 The Bondi mass -- 8.6 Asymptotic behavior of null-outgoing hypersurfaces -- Reference