Non-singular black holes and mass inflation in modified gravity

We analytically derive a class of non-singular, static and spherically symmetric topological black hole metrics in F(R)-gravity. These have not de Sitter core at their centre, as most model standard General Relativity. study the geometric properties motion test particles around these objects. Since they two horizons, inner being Cauchy type, we focus on problem mass inflation show that it occurs except when some extremal conditions are met.