Analytical approximation of the exterior gravitational field of rotating neutron stars

Understand

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.