Energy bounds and ergoregion instability in Einstein-Maxwell-scalar field models

We investigate energy bounds and the stability of stationary asymptotically flat spacetimes with an ergoregion and no future horizon in the context of Einstein-Maxwell-scalar field models that naturally arise in Kaluza-Klein and string theories. In order to do that, we consider scalar field perturbations nonminimally coupled to a background electromagnetic field. We show that there is compactly supported initial data such that the initial energy flux across the initial Cauchy hypersurface is negative and that the energy flux decreases with time. Then, considering arguments due to Friedman and Moschidis, this indicates that the energy flux diverges for those solutions and such spacetimes with an ergoregion are unstable.