We consider a special class of vacuum F(R)-modified gravity models. The
form of their Lagrangian is such that the field equations are trivially
satisfied when the Ricci scalar is constant. There are many interesting
F(R)-models for inflation and dark energy that fall in this class. However,
little is known outside the domain of cosmology therefore we aim to explore the
class of solutions that are static and spherically symmetric. After some
general considerations, we investigate in more detail black hole solutions,
traversable wormhole metrics and, finally, configurations that can match the
anomalous rotation curves of galaxies.Comment: Minor typos corrected, references added. Version accepted for
publication in the European Physical Journal
