Post-Minkowskian closed-form Hamiltonian for gravitating N-body systems

TL;DR

This paper derives a simplified, closed-form Hamiltonian for relativistic N-body gravitational systems in the post-Minkowskian approximation, including all linear gravitational effects, and demonstrates its application to relativistic scattering.

Contribution

It provides the first closed-form Hamiltonian for relativistic N-body systems in the post-Minkowskian approximation, incorporating all linear gravitational terms.

Findings

Hamiltonian expressed in canonical variables only

Includes all special relativistic effects

Applied to relativistic scattering scenarios

Abstract

The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered.