Abstract

FRUTOS-ALFARO, Francisco  and  SOFFEL, Michael. On the post-linear quadrupole-quadrupole metric. Rev. Mat [online]. 2017, vol.24, n.2, pp.239-255. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v24i2.29856.

The Hartle-Thorne metric defines a reliable spacetime for most astrophysical purposes, for instance simulations 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 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 ErezRosen metric to our extended Hartle-Thorne spacetime. It is well known that the Hartle-Thorne solution can be smoothly matched with an interior perfect fluid solution with appropriate physical properties. A comparison among these solutions provides a validation of them. It is clear that in order to represent realistic solutions of self-gravitating (axially symmetric) matter distributions of perfect fluid, the quadrupole moment has to be included as a physical parameter.

Keywords : general relativity; solutions of Einstein’s equations; approximation procedures; weak fields.

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