Universality in static spherically symmetric solutions of f(R) gravity

f ( R ) gravity is a well-known modification of General Relativity, which is used in various models of dark matter and dynamical dark energy. We study static spherically symmetric (SSS) asymptotically flat configurations of the f ( R ) gravity in the Einstein frame for three known scalaron potentials with different asymptotic properties. The main attention is paid to the case of astrophysically relevant configuration mass M and scalaron mass μ greater than several meV , according to existing experimental constraints. This means very large values of the dimensionless (in geometrized units) parameter Mμ , leading to specific properties of the SSS solutions. We consider a sufficiently large size of a scalarization region r 0 ≫ r g , where the space-time metric is essentially different from the Schwarzschild one. It turns out that the scalaron field has universal behavior regardless of Mμ and r 0 and is practically the same for different scalaron potentials. Asymptotic parameters of the metric near the naked singularity at the center of the SSS configuration are obtained analytically for all the models. The test body circular orbits are discussed in view of observational signatures, which can distinguish these configurations from a regular black hole.