A nonanalytic,, quasistationary approximation scheme applied to a model problem

Details A nonanalytic,, quasistationary approximation scheme applied to a model problem A nonanalytic,, quasistationary approximation scheme applied to a model problem

Aug 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982gregr..14..781a&link_type=abstract

General Relativity and Gravitation, vol. 14, Aug. 1982, p. 781-792.

Mathematics

Approximation, Astronomical Models, Cosmology, Gravitational Waves, Functions (Mathematics), Linear Equations, Perturbation Theory, Quasi-Steady States, Wave Equations

Scientific paper

A modification of the standard quasistationary approximation scheme to predict the behavior of gravitationally bound systems is presented which incorporates two of the techniques of singular perturbation theory and removes objections to such schemes. The strained coordinate technique effectively modifies the null cones or characteristics of the problem order by order, and removes logarithmic nonuniformities for large radius in higher order of the scheme for which harmonic coordinates are used. The method of matched asymptotic expansions removes divergent integrals in third post-Newtonian order, instead obtaining finite terms nonanalytic in the expansion parameter. For the model problem, a change of variables in the differential equation is made, corresponding to straining the null coordinate. The approximation method is carried out to the first nonlinear order in the wave zone, demonstrating the cancellation of spurious time-odd terms arising from straining in linear order. Exact pure-frequency solutions to the problem in terms of Whittaker functions are presented.

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