Spherical Symmetric Dyonic Black Holes and Vacuum Geometries in 4 D N=1 Supergravity on Kنhler-ricci Soliton

In this paper we consider several aspects of dyonic non-supersymmetric black holes in fourdimensional N = 1 supergravity coupled to chiral and vector multiplets. The scalar manifold can be considered as a one-parameter family of Kähler manifolds generated by a Kähler–Ricci flow equation. This setup implies that we have a family of dyonic non-supersymmetric black holes deformed with respect to the flow parameter related to the Kähler–Ricci soliton, which possibly controls the nature of black holes, such as their asymptotic and near horizon geometries. We mainly consider two types of black holes, namely a family of dyonic Reissner–Nordströmlike black holes and Bertotti–Robinson-like black holes where the scalars are freezing all over spacetime and at the horizon, respectively. In addition, the corresponding vacuum structures for such black holes are also discussed in the context of Morse–(Bott) theory. Finally, we give some simple CP n -models whose superpotential and gauge couplings have a linear form.