Hartle-Thorne metric
The Hartle-Thorne metric is a spacetime metric in General Relativity describes the exterior of a slowly and rigidly rotating, stationary and axially symmetric body. It is an approximate solution of the vacuum Einstein equations.
The metric was found by James Hartle and Kip Thorne in the 1960s to study the spacetime outside neutron stars, white dwarfs and supermassive stars. It can be shown that it is an approximation to the Kerr metric when the quadrupole moment is set as, which is the correct value for a black hole but not, in general, for other astrophysical objects.Metric
Up to second order in the angular momentum, mass and quadrupole moment, the
metric in spherical coordinates is given by
where
