Can black holes exist in an accelerating universe?

This letter deals with an analysis of the space-time static metric that corresponds to a quintessential state equation with constant characteristic parameter. Following a procedure parallel to as it is used in the case of de Sitter space, we have tried to generalize the metric components that correspond to the quintessential case to also embrace black-hole terms and shown that this is not possible. We argue therefore that, in the absence of a cosmological constant, black holes seem to be prevented in a cosmological space-time which is asymptotically accelerating when the acceleration is driven by a quintessence-like field.