The gravitational frame for solving relativistic N-body problems

Abstract

Abstract This article extends a mechanics-based formulation of relativistic gravitation for two-body systems to N-body systems. The extension is accomplished by applying a gravitational frame—the relativistic linear momentum-free frame of a single interacting pair of bodies, to N-body systems. The relativistic gravitational law is applied pairwise in each gravitational frame, and the resulting accelerations are then Lorentz transformed into a common global frame. As an initial test, rotating rings are modeled as N point sources in prescribed motion. Numerical results confirm the expected presence of transverse deflections of test bodies that are initially approaching the ring radially and the presence of increased attraction due to ring rotation. The mechanics-based formulation applied here to N-body relativistic gravitational problems seeks to achieve computational advantages comparable to those already obtained in nonrelativistic problems.