Escape velocity in general relativity

The problem of determination of the escape velocity in terms of Newton’s gravitational theory and general relativity (GR) is considered. The analysis is performed based on the solution of the equation describing the particle motion along the radial geodesic line. The classical result is derived from the linearized equation for a weak gravitational interaction. A similar result is derived for metric coefficients of space corresponding to the Schwarzschild solution. The relationship determining the escape velocity for the generalized solution leading to metric coefficients having no singularity is also presented.