  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.
