On the Post-linear Quadrupole-Quadrupole Metric

摘要

The Hartle-Thorne metric defines a reliable spacetime for most astrophysicalpurposes, for instance for the simulation of slowly rotating stars. Solving theEinstein field equations, we added terms of second order in the quadrupolemoment to its post-linear version in order to compare it with solutions foundby Blanchet in the frame of the multi-polar post-Minkowskian framework. Wefirst derived the extended Hartle-Thorne metric in harmonic coordinates andthen showed agreement with the corresponding post-linear metric from Blanchet.We also found a coordinate transformation from the post-linear Erez-Rosenmetric to our extended Hartle-Thorne spacetime. It is well known that theHartle-Thorne solution can be smoothly matched with an interior perfect fluidsolution with physically appropriate properties. A comparison among thesesolutions provides a validation of them. It is clear that in order to representrealistic solutions of self-gravitating (axially symmetric) matterdistributions of perfect fluid, the quadrupole moment has to be included as aphysical parameter.