The properties of the dynamics of a single massive particle and a system of massive particles are considered in the Kruskal metric, which is the maximum analytic extension of the Hilbert metric to a gravitating point in a vacuum. It is shown that when describing the motion of particles in the Kruskal metric, dynamic features arise that were not in the analysis of motion in the Schwarzschild metric field.

Lagrangian, Kruskal-Szekeres metric, maximal analytical extension, Hessian

Mathematical problems and theory of numerical methods

Fimin Nikolay Nikolaevich,  ,  orcid.org/0000-0003-2629-5380,  KIAM RAS

Chechetkin Valery Mihailovich,  ,  orcid.org/0000-0002-5241-7962,  KIAM RAS