The post-Minkowski computation for the periodic standing wave approximation

Details The post-Minkowski computation for the periodic standing wave approximation The post-Minkowski computation for the periodic standing wave approximation

Sep 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009phdt........15h&link_type=abstract

Proquest Dissertations And Theses 2009. Section 0240, Part 0606 156 pages; [Ph.D. dissertation].United States -- Utah: The Univ

Mathematics

Standing Wave Approximation, Gravitational Waves, Periodic Standing Waves, Helical Symmetry

Scientific paper

The objective of the present dissertation is to present a novel way to obtain the gravitational waveforms emitted by an idealized binary system consisting of two identical objects in a perfect nondecreasing circular orbit. Since nondecaying orbits are incompatible with the emission of gravitational waves, the model features standing waves coupled with the binary system. These standing waves rotate rigidly at the same angular rate as the sources. Technically the situation is described by the concept of helical symmetry, which effectively reduces the nature of the mathematical problem from a 3+1- D hyperbolic problem to a mixed three-dimensional (3-D) mixed problem. The resulting problem is solved numerically through the use of semispectral methods involving the solution of a system of nonlinear ordinary differential equations in a set of adapted coordinates. The problem is solved using two methods, namely a post-Minkowski approximation and a perturbative method for the full relativistic equations. Results are presented exhibiting the waveforms produced by the idealized binary system.

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