Publications

Abstract

The Hamiltonian description of a system of N bodies interacting by their gravitational field is given in the first-order post-Minkowskian approximation of the General relativity. The bodies are represented by their rest mass, canonical coordinates and momenta. Their velocity is not assumed to be small, as is the case in the post-Newtonian approximation, even particles with zero rest mass moving with the speed of light are allowed. The Hamiltonian given in [4] includes all terms linear in the gravitational constant. It has quite a simple form of a sum of kinetic energies of individual particles and binary interaction potentials. The dynamics of gravitational field is eliminated by solving inhomogeneous wave equations, applying transversetraceless projections, and using the
Routh functional. To illustrate properties and possible applications of the post-Minkowskian Hamiltonian description of system of gravitationally interacting bodies several general-relativistic phenomena are discussed emphasizing the uniform treatment of gravitating and test bodies as well as test photons in this approach.