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System of gravitationally interacting bodies in the postMinkoskian Hamiltonian description

Ledvinka, T.; Schäfer, G.; Bičák, J.

The Hamiltonian description of a system of N bodies in-
teracting 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 mov-
ing with the speed of light are allowed. The Hamilto-
nian given in [4] includes all terms linear in the gravi-
tational constant. It has quite a simple form of a sum
of kinetic energies of individual particles and binary in-
teraction 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 de-
scription of system of gravitationally interacting bodies
several general-relativistic phenomena are discussed em-
phasizing the uniform treatment of gravitating and test
bodies as well as test photons in this approach.
note:Abstract of the talk at 4th Galileo Science Colloquium, December 2013, Prague.
grants:Current problems of gravitation, general relativity and relativistic astrophysics, GAČR 202/09/0772; 2009-2013; hlavní řešitel: Jiří Bičák
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