  Some time ago, the standard geometric framework of Einstein gravity was
extended by gauging the Maxwell algebra as well as the so called AdS-Maxwell
algebra. In this letter it is shown that the actions for these four-dimensional
extended Einstein gravities can be obtained from the five-dimensional
Chern-Simons gravities actions by using the Randall-Sundrum compactification
procedure. It is found that the In\"on\"u-Wigner contraction procedure, in the
Weimar-Woods sense, can be used both to obtain the Maxwell-Chern-Simons action
from the AdS-Maxwell-Chern-Simons action and to obtain the Maxwell extension of
Einstein gravity in 4D from the four-dimensional extended
AdS-Maxwell-Einstein-Hilbert action. It is also shown that the extended
four-dimensional gravities belongs to the Horndeski family of scalar-tensor
theories.
