  We consider modified $f(R)$ gravity with a kinetic curvature scalar as a
chiral self-gravitating model in a spherically symmetric spacetime. Most
attention devoted to finding solutions for special case of scaling
transformation when modified gravity transforms to Einstein frame from Jordan
one. We proposed the method of determination of kinetic function for given
scalar field dependence on space coordinate. New classes of solutions are found
for special choice of $f(R)$ function.
