An observation on the congruence of the expression for escape veolcity in classical mechanics and general relativity in a Schwarzschild metric

In classical mechanics the notion of escape velocity is well defined. In the case of general relativity, this concept is less widely recognised. For instance, the majority of standard teaching texts in this area do not explicitly cover this concept, except in relation to the maximal velocity that a mass-bearing particle may possess and still escape from a body with a strong gravitational field, such as a black hole, derived from the definition of the Schwarschild radius. It is perhaps surprising, that, given the very different approaches of classical mechanics and general relativity in deriving expressions for the escape velocity does have a rigorous meaning within general relativity. In order to preserve the same form as in classical mechanics, it is the velocity required to asymptotically reach infinity, as measured by an observer who is at rest with the respect to the massive body M, who measures an escape velocity corrected by a factor of (1-2GM/c2r)2.