Quadrupole moment of slowly rotating fluid balls

Michael Bradley and Gyula Fodor
Phys. Rev. D 79, 044018 – Published 13 February 2009

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.

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  • Received 6 December 2008

DOI:https://doi.org/10.1103/PhysRevD.79.044018

©2009 American Physical Society

Authors & Affiliations

Michael Bradley1,* and Gyula Fodor2,†

  • 1Department of Physics, Umeå University, SE-901 87 Umeå, Sweden
  • 2KFKI Research Institute for Particle and Nuclear Physics, H-1525, Budapest 114, P.O.B. 49, Hungary

  • *michael.bradley@physics.umu.se
  • gfodor@rmki.kfki.hu

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Vol. 79, Iss. 4 — 15 February 2009

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