On more general Gibbons-Hawking-York boundary terms for f(R) gravity

More general boundary conditions are introduced - with respect to known literature - which produce a well-posed stationary action principle in $f(R)$ gravity. These conditions encompass the known cases, thus enlarging the space of admissible solutions. The corresponding Gibbons-Hawking-York boundary terms are explicitly computed and hold for any analytic f®. The perspectives of application concerning the scalar-tensor mapping and the laws of black-hole thermodynamics are outlined in the conclusions.