On the Post-linear Quadrupole-Quadrupole Metric

Understand

The Hartle-Thorne metric defines a reliable spacetime for most astrophysical purposes, for instance for the simulation of slowly rotating stars.

• Solving the Einstein field equations, we added terms of second order in the quadrupole moment to its post-linear version in order to compare it with solutions found by Blanchet in the frame of the multi-polar post-Minkowskian framework.
• We first derived the extended Hartle-Thorne metric in harmonic coordinates and then showed agreement with the corresponding post-linear metric from Blanchet.
• We also found a coordinate transformation from the post-linear Erez-Rosen metric to our extended Hartle-Thorne spacetime.