Static spacetimes of four dimensional Einstein-Maxwell-Higgs theory with general couplings can be thought of as static black holes and static domain walls. In this paper, we study a static spacetime where the two-surface is in general to be Einstein. In particular, if the scalars are frozen everywhere in the spacetime which can be viewed as the critical points of the black hole and the scalar potentials, then the geometries are of a constant scalar curvature which in general are not Einstein describing charged black holes. Whereas, in the case of charged domain walls the scalars are frozen in the asymptotic region describing spaces of constant scalar curvature.
Topics
Black holes
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