A no-hair theorem for spherically symmetric black holes in $R^2$ gravity

Understand

In a recent paper Ca\~nate (CQG, {\bf 35}, 025018 (2018)) proved a no hair theorem to static and spherically symmetric or stationary axisymmetric black holes in general $f(R)$ gravity.

• The theorem applies for isolated asymptotically flat or asymptotically de Sitter black holes and also in the case when vacuum is replaced by a minimally coupled source having a traceless energy momentum tensor.
• This theorem excludes the case of pure quadratic gravity, $f(R) = R^2$.
• In this paper we use the scalar tensor representation of general $f(R)$ theory to show that there are no hairy black hole in pure $R^2$ gravity.