  The gravitation equations of the general relativity, written for Riemannian
space-time geometry, are extended to the case of arbitrary (non-Riemannian)
space-time geometry. The obtained equations are written in terms of the world
function in the coordinateless form. These equations determine directly the
world function, (but not only the metric tensor). As a result the space-time
geometry appears to be non-Rieamannian. Invariant form of the obtained
equations admits one to exclude influence of the coordinate system on solutions
of dynamic equations. Anybody, who trusts in the general relativity, is to
accept the extended general relativity, because the extended theory does not
use any new hypotheses. It corrects only inconsequences and restrictions of the
conventional conception of general relativity. The extended general relativity
predicts an induced antigravitation, which eliminates existence of black holes.
