On the metric of the gravitational field of a point mass for stationary observers

Abstract

Aim. The work is performed with the aim of obtaining an approximate expression for the space-time metric of the centrally symmetric gravitational field of a point mass, which is a generalization of the Schwarzschild metric for stationary observers located at any non-zero distance from the point mass.

Methodology. The analysis was carried out, the structure of the Schwarzschild metric and the dependence of the components of the metric tensor on the potential difference of the gravitational field were used, which is one of the main provisions of the general theory of relativity.

Results. An approximate expression for the space-time metric of the centrally symmetric gravitational field of a point mass is obtained, which is a generalization of the Schwarzschild metric for the case of stationary observers located at any non-zero distance from the point mass. The resulting metric asymptotically tends to the Schwarzschild metric as the observer moves away from the point mass and is, at least, the first post-Newtonian approximation to the exact solution.

Research implications. Analysis of the obtained expression for the space-time metric of the centrally symmetric gravitational field of a point mass allows us to conclude that the relative horizons of visibility for observers with finite radial coordinates are located on spheres with radial coordinates smaller than the gravitational radius.