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 often called nowadays Galileon theory. We will examine a particular sub class 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 for the first time regular scalar tensor black holes with a non trivial scalar field.
