Spherically symmetric black holes in $f(R)$ gravity: Is geometric scalar hair supported ?

Understand

We discuss with a rather critical eye the current situation of black hole (BH) solutions in $f(R)$ gravity and shed light about its geometrical and physical significance.

• We also argue about the meaning, existence or lack thereof of a Birkhoff's theorem in this kind of modified gravity.
• We focus then on the analysis and quest of $non-trivial$ (i.e.
• hairy) $asymptotically\,\,flat$ (AF) BH solutions in static and spherically symmetric (SSS) spacetimes in vacuum having the property that the Ricci scalar does $not$ vanish identically in the domain of outer communication.