Advanced General Relativity
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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2-surface ABCD affine parameter algebra appendix asymptotically Bianchi identities Bondi Bondi mass Cauchy problem caustic characteristic initial value choose commutator components condition conformal congruence consider const constant construction coordinate chart coordinate system covector curvature defined definition denoted dependent variables differential equivalent Exercise exists field equations follows frame function gauge freedom given gravitational holomorphic hypersurface implies inertial integral curve isomorphic Legendrian lemma linear matrix Maxwell equations metric Minkowski spacetime neighbourhood NP scalars null directions null geodesics null hypersurface null vector orthogonal parallelly Penrose and Rindler physical Proof propagate PT'M quasilinear Ricci Ricci identities satisfied scalar field self-intersection line Show smooth solution spacelike vector special relativity spin basis spin weight Suppose surface symmetric spinors tangent vector tensor tetrad theorem theory timelike geodesics torsion Tp(M transformation unphysical vacuum valence vanishes vector field vector space wave Weyl Weyl spinor
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Quantum Gravity, Quantum Cosmology and Lorentzian Geometries
Limited preview - 1994