Scalar fields and Lifshitz black holes from Derrick's theorem evasion

We study classical scalar fields in asymptotically Lifshitz spacetimes. By evading Derrick’s theorem requiring the scalar potential to explicitly depend on the background coordinates, we induce a diffeomorphism invariance breaking and settle a first-order formalism to find spatially localized solutions in the probe field limit. By inserting a backreaction equipped with a cosmological constant and a Maxwell term coupled to a dielectric function in the model, we find a Lifshitz black hole solution.