On quasi-topological electromagnetism and black holes

In this paper we extend the quasi-topological electromagnetism, recently introduced in arXiv:1907.10876v1 [hep-th], to arbitrary dimensions by introducing a fundamental $p$--form field. This allows to construct new dyonic black hole solutions in odd-dimensions, as well as regular $D$--dimensional black holes and solitons. The three--dimensional system consists of a Maxwell field interacting with a scalar field, leading to a deformation of the BTZ black hole. We present the general formulae defining the black hole solutions in arbitrary dimensions in Lovelock theory and explore the thermal properties of the asymptotically AdS black holes in the gravitational framework of General Relativity. In five dimensions, the latter black holes possess a rich phase space structure in the canonical ensemble, giving rise to as many as five different black hole phases at a fixed temperature, for a given range of the parameters.