Schwarzschild Solution in R-spacetime

Abstract

Here we construct new solution for the Einstein equations -- some analog of the Schwarzschild metric in anti--de Sitter--Beltrami space in the $c\to \infty$ limit ($R$-space). In this case we derive an adiabatic invariant for finite movement of the massive point particle and separate variables Hamilton--Jacobi equation. Quasi orbital motion is analyzed and its radius time dependence is obtained.