  It is known that B\"acklund transformations can be used to generate
stationary axisymmetric solutions of Einstein's vacuum field equations with any
number of constants. We will use this class of exact solutions to describe the
exterior vacuum region of numerically calculated neutron stars. Therefore we
study how an Ernst potential given on the rotation axis and containing an
arbitrary number of constants can be used to determine the metric everywhere.
Then we review two methods to determine those constants from a numerically
calculated solution. Finally, we compare the metric and physical properties of
our analytic solution with the numerical data and find excellent agreement even
for a small number of parameters.
