The spherical symmetry Black hole collapse in expanding universe
  The spherical symmetry Black holes are considered in expanding background. The singularity line and the marginally trapped tube surface behavior are discussed. In particular, we address the conditions of whether a dynamical horizon forms for these cosmological black holes. We also discuss the cosmological constant effect on these black holes and the redshift of the light which comes from the marginally trapped tube surface. 
J. T. Firouzjaee
gr-qc astro-ph.GA