| Resumo: | We review recent results on the existence of static black holes (BHs) without spatial isometrics in four spacetime dimensions and propose a general framework for their study. These configurations are regular on and outside a horizon of spherical topology. Two different mechanisms allowing for their existence are identified. The first one relies on the presence of a solitonic limit of the BHs; when the solitons have no spatial isometrics, the BHs, being a nonlinear bound state between the solitons and a horizon, inherit this property. The second one is related to BH scalarization, and the existence of zero modes of the scalar field without isometrics around a spherical horizon. When the zero modes have no spatial isometrics, the back-reaction of their nonlinear continuation makes the scalarized BHs inherit the absence of spatial continuous symmetries. A number of general features of the solutions are discussed together with possible generalizations.
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