We consider metric $f(R)$ theories of gravity without mapping them to their scalar-tensor counterpart, but using the Ricci scalar itself as an “extra” degree of freedom. This approach avoids then the introduction of a scalar-field potential that might be ill defined (not single valued). In order to explicitly show the usefulness of this method, we focus on static and spherically symmetric spacetimes and deal with the recent controversy about the existence of extended relativistic objects in certain class of $f(R)$ models.

• Received 29 June 2010

DOI:https://doi.org/10.1103/PhysRevD.83.024039