Hamiltonian two-body system in special relativity

Abstract

We consider an isolated system made of two pointlike bodies interacting at a distance in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on the equal-time condition. The center of mass is rather a center of energy. Individual energies are separately conserved and the meaning of their positivity is discussed in terms of world-lines. Several results derived decades ago under restrictive assumptions are extended to the general case. Relative motion has a structure similar to that of a nonrelativistic one-body motion in a stationnary external potential, but its evolution parameter is generally not a linear function of the center-of-mass time, unless the relative motion is circular (in this latter case the motion is periodic in the center-of-mass time). Finally the case of an extreme mass ratio is investigated. When this ratio tends to zero the heavy body coincides with the center of mass provided that a certain first integral, related to the binding energy is not too large.

25 pages, substantial revision, errors corrected, one section and several references added

References in corpus (4)

• Centers of Mass and Rotational Kinematics for the Relativistic N-Body Problem in the Rest-Frame Instant Form
• Hamiltonian Relativistic Two-Body Problem: Center of Mass and Orbit Reconstruction
• Post-Minkowski action for point particles and a helically symmetric binary solution
• Relativistic non-instantaneous action-at-a-distance interactions

Cited by in corpus (1)

• Relative motion in spacetime