Magnetic and electric black holes in arbitrary dimensions

In this work, we compare two different objects: electric black holes and magnetic black holes in arbitrary dimension. The comparison is made in terms of the corresponding moduli space and their extremal geometries. We treat parallelly the magnetic and the electric cases. Specifically, we discuss the gravitational solution of these spherically symmetric objects in the presence of a positive cosmological constant. Then, we find the bounded region of the moduli space allowing the existence of black holes. After identifying it in both the electric and the magnetic case, we calculate the geometry that comes out between the horizons at the coalescence points. Although the electric and magnetic cases are both very different (only dual in four dimensions), gravity solutions seem to clear up most of the differences and lead to very similar geometries.