Choreographic solution to the general relativistic three-body problem

TL;DR

This paper investigates whether choreographic solutions like the figure-eight orbit, known in Newtonian gravity, can exist in the general relativistic three-body problem by examining relativistic corrections to initial conditions.

Contribution

The study demonstrates that a choreographic figure-eight orbit can be realized in general relativity through careful adjustments of initial conditions, suggesting such solutions are possible beyond Newtonian physics.

Findings

Choreographic solutions can exist in general relativity with proper initial conditions

Relativistic corrections enable closed orbits similar to Newtonian figure-eight

Potential for discovering new choreographic solutions in relativistic N-body systems

Abstract

We revisit 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 particles move 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 re-discovered with its existence proof by Chenciner and Montgomery (2000). In general relativity, however, the periastron shift prohibits a binary system from orbiting in a single closed curve. Therefore, it is unclear whether general relativistic effects admit a choreographic solution such as the figure eight. We carefully examine general relativistic corrections to initial conditions so that an orbit for a three-body system can be closed and a figure eight. This solution is still choreographic. This illustration suggests that the general relativistic N-body problem also may admit a certain class of choreographic solutions.