Spherical steady accretion flows -- dependence on the cosmological constant, exact isothermal solutions and applications to cosmology

We investigate spherical, isothermal and polytropic steady accretion models in the presence of the cosmological constant. Exact solutions are found for three classes of isothermal fluids, assuming the test gas approximation. The cosmological constant damps the mass accretion rate and - above certain limit - completely stops the steady accretion onto black holes. A “homoclinic-type” accretion flow of polytropic gas has been discovered in AdS spacetimes in the test-gas limit. These results can have cosmological connotation, through the Einstein–Straus vacuole model of embedding local structures into Friedman-Lemaitre-Robertson-Walker spacetimes. In particular one infers that steady accretion would not exist in the late phases of the Penrose’s scenario of the evolution of the Universe, known as the Weyl curvature hypothesis.