On the Escape Velocity in General Relativity and the Problem of Dark Matter

The paper is concerned with analysis of the escape velocity for a spherical star within the framework of the Classical Gravitation Theory (CGT) and the General Theory of Relativity (GTR). In GTR, two possible results corresponding to the classical and the generalized Schwarzschild solutions are obtained. For the latter solution which, in contrast to the former one, is not singular, the critical radius of the star for which the particle cannot leave the surface even if the initial velocity of the particle is equal to the velocity of light is found and is associated with the radius of the Dark Star introduced in the 18-th century by J. Michel and P. Laplace. As shown, the radius of the largest visible star, i.e., the red supergiant UY Scutti, is much larger than the obtained critical radius. If the Dark Stars whose radii are smaller than the critical radius exist, they are hypothetically not visible and can concentrate the matter that cannot be observed.