Post-Newtonian Lagrangian of an N-body System with Arbitrary Mass and Spin Multipoles

TL;DR

This paper derives a comprehensive post-Newtonian Lagrangian for an N-body system with arbitrary mass and spin multipoles in scalar-tensor gravity, crucial for precise gravitational waveform modeling of inspiraling binaries.

Contribution

It generalizes existing Lagrangians to include higher multipoles and accounts for their dynamic evolution, enhancing modeling accuracy for complex astrophysical systems.

Findings

Derived the post-Newtonian Lagrangian for arbitrary multipoles.

Enabled more accurate gravitational waveform calculations.

Facilitated formulation of conservation laws in N-body systems.

Abstract

The present paper derives the post-Newtonian Lagrangian of translational motion of N arbitrary-structured bodies with all mass and spin multipoles in a scalar-tensor theory of gravity. The multipoles depend on time and evolve in accordance with their own dynamic equations of motion. The Lagrangian is retrieved from the post-Newtonian equations of motion by solving the inverse problem of the Lagrangian mechanics and generalizes a well-known Lagrangian of pole-dipole-quadrupole massive particles to the particles of higher multipolarity. Analytic treatment of the higher-order multipole contributions is important for more rigorous computation of gravitational waveform of inspiralling compact binaries at the latest stage of their orbital evolution before merger when tidal and rotational deformations of stars are no longer small and rapidly change in time. The Lagrangian of an N-body system with arbitrary mass and spin multipoles is instrumental for formulation of the post-Newtonian conservation laws of energy, momenta and the integrals of the center of mass.