Astrophysical Black Hole horizons in a cosmological context: Nature and   possible consequences on Hawking Radiation
  This paper considers the nature of apparent horizons for astrophysical black hole situated in a realistic cosmological context. Using semi-tetrad covariant methods we study the local evolutions of the boundaries of the trapped region in the spacetime. For a collapsing massive star immersed in a cosmology with Cosmic Background Radiation (CBR), we show that the initial 2 dimensional marginally trapped surface bifurcates into inner and outer horizons. The inner horizon is timelike while the continuous CBR influx into the black hole makes the outer horizon spacelike. We discuss the possible consequences of these features for Hawking radiation in realistic astrophysical contexts. 
George F R Ellis, Rituparno Goswami, Aymen I. M. Hamid and Sunil D.   Maharaj
gr-qc hep-th