Radiative gravitational fields in general relativity. I - General structure of the field outside the source

Astronomy and Astrophysics – Astrophysics

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Astrophysics, Gravitational Fields, Relativity, Convergence, Coordinate Transformations, Far Fields, Green'S Functions, Linear Equations, Near Fields, Tensor Analysis, Vacuum

Scientific paper

A well-defined formal framework is presented, together with appropriate mathematical tools, to allow the implementation in a constructive way, and the investigation in full mathematical details, of the Bonnor-Thorne approach to gravitational radiation theory. It is shown how to construct, within this framework, the general radiative (formal) solution of the Einstein vacuum equations, in harmonic coordinates, which is both past-stationary and past-asymptotically Minkowskian. The structure of the latter general radiative metric (including all tails and nonlinear effects) is investigated both in the near zone and in the far zone. As a side result it is proven that post-Newtonian expansions must be done by using the gauge functions (lg c) exp p/c exp n (p, n = positive integers).

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