Abstract
We present a detailed analysis of a rotating black hole surrounded by “quintessence.” This solution represents a fluid with a constant equation of state, [Formula: see text], which can for example describe an effective warm dark matter fluid around a black hole. We clarify the conditions for the existence of such a solution and study its structure by analyzing the existence of horizons as well as the extremal case. We show that the deflection angle produced by the black hole depends on the parameters [Formula: see text] which need to obey the condition [Formula: see text] because of the weak energy condition, where [Formula: see text] is an additional parameter describing the hair of the black hole. In this context, we found that for [Formula: see text] (consistent with warm dark matter) and [Formula: see text], the deviation angle is larger than that in the Kerr space–time for direct and retrograde orbits. We also derive an exact solution in the case of [Formula: see text].
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