Relativistic Euler’s three-body problem, optical geometry, and the golden ratio

Relativistic Euler’s 3-body problem, optical geometry and the golden ratio

A Weyl solution describing two Schwarzschild black holes is considered. We focus on the Z2 invariant solution, with ADM mass MADM = 2MK , where MK is the Komar mass of each black hole. For this solution the set of fixed points of the discrete symmetry is a totally geodesic sub-manifold. The existence and radii of circular photon orbits in this sub-manifold are studied, as functions of the dista...

Solution of a Relativistic Three Body Problem

Starting from a relativistic s-wave scattering length model for the two particle input we construct an unambiguous, unitary solution of the relativistic three body problem given only the masses ma,mb,mc and the masses of the two body bound states μbc, μca, μab. Submitted to Few Body Systems: Tjon Festschrift Issue; revised ms. resubmitted October, 1997 Work supported by Department of Energy con...

Applications of Lobachevsky Geometry to the Relativistic Two-Body Problem

In this talk we consider the geometrical basis for the reduction of the relativistic 2-body problem, much like the non-relativistic one, to describing the motion of an effective particle in an external field. It is shown that this possibility is deeply related with the Lobachevsky geometry. The concept of relativistic reduced mass and effective relativistic particle is discussed using this geom...

Choreographic solution to the general-relativistic three-body problem.

We reexamine the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particle moves periodically in a single closed orbit. One is a stable figure-eight orbit for a three-body system, which was found first by Moore (1993) and rediscovered with its existence proof by Chenc...

Problem of Erdös – Vershik for Golden Ratio