Advanced General RelativityCambridge University Press, 26. nóv. 1993 - 228 síður A modern self-contained introduction to key topics in advanced general relativity. The opening chapter reviews the subject, with strong emphasis on the geometric structures underlying the theory. The next chapter discusses 2-component spinor theory, its usefulness for describing zero-mass fields, its practical application via Newman-Penrose formalism, together with examples and applications. The subsequent chapter is an account of the asymptotic theory far from a strong gravitational source, describing the mathematical theory by which measurements of the far-field and gravitational radiation emanating from a source can be used to describe the source itself. The final chapter describes the natural characteristic initial value problem, first in general terms, and then with particular emphasis for relativity, concluding with its relation to Arnold's singularity theory. Exercises are included. |
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ABA'B ABCD affine parameter algebra asymptotically Bianchi identities Bondi Bondi mass Cauchy problem caustic characteristic initial value choose coefficients commutator complex components conformal congruence connection consider const constant coordinate system covector defined definition denoted dependent variables derivative differential ds² equivalent Exercise exists field equations follows function gauge gauge freedom given gravitational hypersurface implies inertial integral curve Lagrangian Legendrian lemma linear manifold matrix Maxwell equations metric Minkowski spacetime neighbourhood NP scalars null geodesics null vector O(N³ orthogonal P₁ Penrose and Rindler Proof propagate quasilinear Ricci Ricci identities satisfied scalar field self-intersection line Show smooth solution spacelike spacelike vector special relativity spin basis spin weight Suppose symmetric spinors symplectic tangent vector tensor tetrad theorem theory transformation vacuum valence vanishes vector field vector space wave Weyl მე