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In this paper we show that, for general scalar fields, stationaryconfigurations are possible for shift symmetric theories only. This symmetrywith respect to constant translations in field space should either be manifestin the original field variables or reveal itself after an appropriate fieldredefinition. In particular this result implies that neither k-Essence norQuintessence can have exact steady state / Bondi accretion onto Black Holes. Wealso discuss the role of field redefinitions in k-Essence theories. Here westudy the transformation properties of observables and other variables ink-Essence and emphasize which of them are covariant under field redefinitions.Finally we find that stationary field configurations are necessarily linear inKilling time, provided that shift symmetry is realized in terms of these fieldvariables.

Stationary Configurations Imply Shift Symmetry: No Bondi Accretion for Quintessence / k-Essence