Waveless Approximation Theories of Gravity

TL;DR

This paper introduces waveless approximation theories (WAT) that simplify Einstein's equations by suppressing gravitational waves, enabling easier analysis of multibody systems while maintaining accurate matter evolution.

Contribution

The paper develops new waveless approximation theories that replace complex wave dynamics with elliptic equations, simplifying Einstein's equations for multibody systems.

Findings

WAT suppresses gravitational radiation effectively.

WAT provides accurate matter evolution compared to full Einstein solutions.

Simplifies analysis of complex multibody gravitational systems.

Abstract

The analysis of a general multibody physical system governed by Einstein's equations in quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties -- many coupled degrees of freedom, dynamic instability -- are associated with the presence of gravitational waves. We have developed a number of ``waveless approximation theories'' (WAT) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.