Exact Solutions in Higher-Dimensional Lovelock and $AdS_5$ Chern-Simons Gravity

Lovelock gravity in $D$-dimensional space-times is considered adopting Cartan's structure equations. In this context, we find out exact solutions in cosmological and spherically symmetric backgrounds. In the latter case, we also derive horizons and the corresponding Bekenstein--Hawking entropies. Moreover, we focus on the topological Chern--Simons theory, providing exact solutions in 5 dimensions. Specifically, it is possible to show that Anti-de Sitter invariant Chern--Simons gravity can be framed within Lovelock--Zumino gravity in 5 dimensions, for particular choices of Lovelock parameters.