  We examine the statistical number of states, from which statistical entropy
can be derived, and we show that it is an explicit function of the metric and
thus observer dependent. We find a constraint on a transformation of the metric
that preserves the number of states but does not preserve curvature. In showing
exactly how curvature independence arises in the conventional definition of
statistical entropy, we gain a precise understanding of the direction in which
it needs to be redefined in the treatment of black hole entropy.
