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We study the chiral self-gravitating model (CSGM) of a special type in thespherically symmetric static spacetime in Einstein frame. Such CSGM is derived,by virtue of Weyl conformal transformation, from a gravity model in the Jordanframe corresponding to a modified $f(R)$ gravity with a kinetic scalarcurvature. We investigate the model using harmonic coordinates and consider aspecial case of the scaling transformation from the Jordan frame. We findclasses of solutions corresponding to a zero potential and we investigatehorizons, centers and the asymptotic behavior of the obtained solutions. Otherclasses of solutions (for the potential not equal to zero) are found using aspecial relation (ansatz) between the metric components. Investigations ofhorizons, centers and asymptotic behavior of obtained solutions for this newcase are performed as well. Comparative analysis with the solutions obtainedearlier in literature is made.

Black holes and wormholes in $f(R)$ gravity with a kinetic curvature scalar