Waveless Approximation Theories of Gravity

During the 1970’s, there was a lot of interest in developing good numerical simulations of the production of gravitational radiation by strongly interacting astrophysical systems (the archetype being a binary pair of black holes). As a graduate student at the University of Maryland during that time, with strong encouragement from my advisor, Charles Misner, I developed a collection of approximation schemes which were designed to try to avoid the fatal numerical instabilities which arose during the course of all of the contemporary attempts to evolve the full system of Einstein’s equations. The idea of these schemes was to mathematically decouple the “gravitational wave ” production from the evolution of the matter and the slowly changing “induced gravitational fields ” of the astrophysical systems. The equations governing the evolution of the matter and induced gravitational field system were designed to be a form of enhanced Newton-Euler system: The matter fields would evolve via Euler-type equations, while the induced gravitational fields would be determined by a system of elliptic equations to be solved for certain pieces of the metric. These equations were set up to ignore gravitational radiation, except for the possible inclusion of terms accounting for the loss of energy due to wave propagation. To determine the gravitational radiation production, the idea was to incorporate the motion of the matter and induced gravitational fields into source terms for a system of linear wave equations. 1 In 1978, I wrote a paper which describes some of the equation systems I developed for the matter and induced gravitational field evolution. I called these systems ”Waveless Approximation Theories of Gravity”, and I submitted a paper with this title to Physical Review D. It was rejected by the referees, based on the reasonable contention that I hadn’t tried to numerically implement the ideas. Not being any good at numerical work, I lay the paper and the ideas aside, and I went on to other things. The only record of it which I left was a brief mention towards the end of an article I wrote with Jim Nester for the Einstein Centenary volume ”General Relativity and

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