  The BSSN and standard gauge equations are written in covariant form with
respect to spatial coordinate transformations. The BSSN variables are defined
as tensors with no density weights. This allows us to evolve a given set of
initial data using two different coordinate systems and to relate the results
using the familiar tensor transformation rules. Two variants of the covariant
equations are considered. These differ from one another in the way that the
determinant of the conformal metric is evolved.
