The gravitation equations of the general relativity, written for Riemannian spacetime 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). Asa result the space-time geometry appears to be non-Rieamannian. Invariant form of theobtained equations admits one to exclude influence of the coordinate system on solutions ofdynamic equations. Anybody, who trusts in the general relativity, is to accept the extendedgeneral relativity, because the extended theory does not use any new hypotheses. It correctsonly inconsequences and restrictions of the conventional conception of general relativity. Theextended general relativity predicts an induced antigravitation, which eliminates existence ofblack holes.
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