f(R) theory of gravity and conformal continuations

We consider static, spherically symmetric vacuum solutions to the equations of a theory of gravity with the Lagrangian f(R) where R is the scalar curvature and f is an arbitrary function. Using a well-known conformal transformation, the equations of f(R) theory are reduced to the ``Einstein picture'', i.e., to the equations of general relativity with a source in the form of a scalar field with a potential. We have obtained necessary and sufficient conditions for the existence of solutions admitting conformal continuations. The latter means that a central singularity that exists in the Einstein picture is mapped, in the Jordan picture (i.e., in the manifold corresponding to the original formulation of the theory), to a certain regular sphere, and the solution to the field equations may be smoothly continued beyond it. The value of the curvature R on the transition sphere corresponds to an extremum of the function f(R). Specific examples are considered.