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The evolution of the mass of a black hole embedded in a universe filled withdark energy and cold dark matter is calculated in a closed form within a testfluid model in a Schwarzschild metric, taking into account the cosmologicalevolution of both fluids. The result describes exactly how accretionasymptotically switches from the matter-dominated to the Lambda-dominatedregime. For early epochs, the black hole mass increases due to dark matteraccretion, and on later epochs the increase in mass stops as dark energyaccretion takes over. Thus, the unphysical behaviour of previous analyses isimproved in this simple exact model.

Analytical solutions of accreting black holes immersed in a Lambda-CDM model