## Advanced General RelativityA 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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ABCD appendix assume asymptotically basis becomes Bianchi identities called caustic characteristic chart choice choose Clearly coefficients commutator complex components condition conformal connection consider const constant construction coordinate coordinate system corresponding curve defined definition denoted dependent derivative described differential direction discussion element energy equation equivalent example Exercise exists field equations Finally follows frame function further geodesic given gives gravitational holds hypersurface identity implies indices initial integral introduce lemma linear manifold mass metric Minkowski normal Note null null vector obtain physical problem projection Proof properties quantities relativity represents require respect result satisfied scalar Show smooth solution space spacelike spacetime special relativity spin spinor standard structure Suppose surface symmetric tangent vector tensor tetrad theorem theory timelike transformation usually vanishes variables vector field wave