  We present an alternative scheme of finding apparent horizons based on
spectral methods applied to Robinson-Trautman spacetimes. We have considered
distinct initial data such as representing the spheroids of matter and the
head-on collision of two non-rotating black holes. The evolution of the
apparent horizon is presented. We have obtained in some cases a mass gap
between the final Bondi and apparent horizon masses, whose implications were
briefly commented in the light of the thermodynamics of black holes.
