Black hole for the Einstein-Chern-Simons gravity

We consider a five-dimensional action which is composed of a gravitational sector and a sector of matter, where the gravitational sector is given by a Einstein-Chern-Simons gravity action instead of the Einstein-Hilbert action. We obtain the Einstein-Chern-Simons (EChS) field equations together with their spherically symmetric solution, which lead, in certain limit, to the standard five-dimensional solution of the Einstein-Cartan field equations. The conditions are found under which the EChS field equations admit black hole type solutions. The maximal extension and conformal compactification are also studied.