Abstract
The solutions of the General Relativity equations with quadratic LagrangiansR iklmRiklm, RikRik, R2 are studied. It is shown that nontrivial Euclidian (atr → ∞) solution of the theory equations does not exist whenT≠0 (T is a trace of the energy-momentum tensor of matter). The Schwarzschild solution is not an external part of a total solution whenT≠0. Under conditionT=R=0 LagrangiansR iklmRiklm, RikRik lead to the identical field equations, so there exist the only quadratic Lagrangian and the only field equations. This equation has a solution with an external part being a standard Schwarzschild solution for the statical spherically symmetric case.
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