  We shed some light on the field theory interpretation of C-metric by
investigating the minimal surfaces which are homologous to the given boundary
regions. The accelerating black holes change the asymptotic structure of the
space-time. We focus on the geometry features of the minimal surface and study
how deep it reaches into the bulk. The regularized area of the minimal surface
is not well defined and we introduce a new quantity $D(m,\theta_0)$, defined as
the minimal surface divided by the area of the given boundary region, to study
the system.
