The quadrupole moment of slowly rotating fluid balls

Abstract

In this paper we use the second order formalism of Hartle to study slowly and rigidly rotating stars with focus on the quadrupole moment of the object. The second order field equations for the interior fluid are solved numerically for different classes of possible equations of state and these solutions are then matched to a vacuum solution that includes the general asymptotically flat axisymmetric metric to second order, using the Darmois-Israel procedure. For these solutions we find that the quadrupole moment differs from that of the Kerr metric, as has also been found for some equations of state in other studies. Further we consider the post-Minkowskian limit analytically. In the paper we also illustrate how the relativistic multipole moments can be calculated from a complex gravitational potential.

arXiv comment13 pages, 5 figures

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• An approximate global solution of Einstein's equation for a rotating compact source with linear equation of state
• On the equivalence of approximate stationary axially symmetric solutions of Einstein field equations
• Wahlquist's metric versus an approximate solution with the same equation of state
• On the multipole moments of a rigidly rotating fluid body