Gravitating monopoles and black holes in the Einstein–Born–Infeld–Higgs model

We find static spherically symmetric monopoles in the Einstein–Born–Infeld–Higgs model in 3+1 dimensions. The solutions exist only when a parameter α (related to the strength of Gravitational interaction) does not exceed certain critical value. We also discuss magnetically charged non Abelian black holes in this model. We analyse these solutions numerically.