The Lagrange Equilibrium Points L_4 and L_5 in a Black Hole Binary System

TL;DR

This paper investigates how gravitational radiation affects the positions and stability of L_4 and L_5 Lagrange points in a black hole binary system, with implications for electromagnetic signals accompanying gravitational waves.

Contribution

It provides the first analysis of L_4 and L_5 stability and location changes in a black hole binary due to gravitational radiation effects.

Findings

L_4 moves closer to the secondary mass and becomes less stable.

L_5 moves away from the secondary and becomes more stable.

Results have implications for electromagnetic counterparts to gravitational waves.

Abstract

We calculate the location and stability of the L_4 and L_5 Lagrange equilibrium points in the circular restricted three-body problem as the binary system evolves via gravitational radiation losses. Relative to the purely Newtonian case, we find that the L_4 equilibrium point moves towards the secondary mass and becomes slightly less stable, while the L_5 point moves away from the secondary and gains in stability. We discuss a number of astrophysical applications of these results, in particular as a mechanism for producing electromagnetic counterparts to gravitational-wave signals.