We will review modified gravity theories and in particular scalar tensor
theories, the mildest of modifications, where we have an additional
interacting scalar field coupling to the metric tensor. By means of a
theorem given by Horndeski back in 1974 we will show the most general of
these theories. We will examine a particular subclass of Horndeski theory
which has interesting properties with respect to the cosmological constant
problem. This carries the unfortunate name fab 4. We will then find black
hole solutions of this subclass which in some cases will be identical to
GR solutions. The novel ingredient will be the presence of a time and
space dependent scalar. As we will see time dependence will birfucate no
hair theorems and provide regular scalar tensor black holes with a non
trivial scalar field.
