Schwarzschild Solution in R-spacetime

TL;DR

This paper constructs an analog of the Schwarzschild solution in R-spacetime, deriving an adiabatic invariant and analyzing quasi-orbital motion in this new gravitational context.

Contribution

It introduces a novel Schwarzschild-like solution in R-spacetime and analyzes particle dynamics within this framework, extending classical solutions to new spacetime geometries.

Findings

Derived an adiabatic invariant for particle motion in R-spacetime.

Separated variables in the Hamilton-Jacobi equation for this spacetime.

Analyzed the radius-time dependence of quasi-orbital motion.

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.