Derrick's theorem in curved spacetime

We extend Derrick's theorem to the case of a generic irrotational curved spacetime adopting a strategy similar to the original proof. We show that a static relativistic star made of real scalar fields is never possible regardless of the geometrical properties of the (static) spacetimes. The generalized theorem offers a tool that can be used to check the stability of localized solutions of a number of types of scalar field models as well as of compact objects of theories of gravity with a nonminimally coupled scalar degree of freedom.