2012ApJ...756...82P

Whether or not analytic exact vacuum (electrovacuum) solutions of the Einstein (Einstein-Maxwell) field equations can accurately describe the exterior space-time of compact stars still remains an interesting open question in relativistic astrophysics. As an attempt to establish their level of accuracy, the radii of the innermost stable circular orbits (ISCOs) of test particles given by analytic exterior space-time geometries have been compared with those given by numerical solutions for neutron stars (NSs) obeying a realistic equation of state (EOS). It has been so shown that the six-parametric solution of Pachón et al. (PRS) more accurately describes the NS ISCO radii than other analytic models do. We propose here an additional test of accuracy for analytic exterior geometries based on the comparison of orbital frequencies of neutral test particles. We compute the Keplerian, frame-dragging, and precession and oscillation frequencies of the radial and vertical motions of neutral test particles for the Kerr and PRS geometries and then compare them with the numerical values obtained by Morsink & Stella for realistic NSs. We identify the role of high-order multipole moments such as the mass quadrupole and current octupole in the determination of the orbital frequencies, especially in the rapid rotation regime. The results of this work are relevant to cast a separatrix between black hole and NS signatures and to probe the nuclear-matter EOS and NS parameters from the quasi-periodic oscillations observed in low-mass X-ray binaries.