Realistic fluids as source for dynamically accreting black holes in a   cosmological background
  We show that a single imperfect fluid can be used as a source to obtain the generalized McVittie metric as an exact solution to Einstein's equations. The mass parameter in this metric varies with time thanks to a mechanism based on the presence of a temperature gradient. This fully dynamical solution is interpreted as an accreting black hole in an expanding universe if the metric asymptotes to Schwarzschild-de Sitter at temporal infinity. We present a simple but instructive example for the mass function and briefly discuss the structure of the apparent horizons and the past singularity. 
Daniel C. Guariento, Michele Fontanini, Alan M. da Silva, Elcio   Abdalla
gr-qc astro-ph.CO