Realistic Exact Solution for the Exterior Field of a Rotating Neutron Star

TL;DR

This paper introduces a new six-parameter exact solution to Einstein-Maxwell equations that models the exterior field of rotating, deformed, magnetized, charged neutron stars, and demonstrates its superior accuracy in matching numerical interior solutions and ISCO radii.

Contribution

It presents a novel six-parameter exact solution for the exterior field of neutron stars, incorporating multipole moments and electromagnetic fields, and validates its accuracy against numerical models.

Findings

The solution accurately matches numerical interior models of neutron stars.

It provides better ISCO radius predictions than previous models.

The solution encompasses arbitrary physical parameters including charge and magnetic dipole.

Abstract

A new six-parametric, axisymmetric and asymptotically flat exact solution of Einstein-Maxwell field equations having reflection symmetry is presented. It has arbitrary physical parameters of mass, angular momentum, mass--quadrupole moment, current octupole moment, electric charge and magnetic dipole, so it can represent the exterior field of a rotating, deformed, magnetized and charged object; some properties of the closed-form analytic solution such as its multipolar structure, electromagnetic fields and singularities are also presented. In the vacuum case, this analytic solution is matched to some numerical interior solutions representing neutron stars, calculated by Berti & Stergioulas (Mon. Not. Roy. Astron. Soc. 350, 1416 (2004)), imposing that the multipole moments be the same. As an independent test of accuracy of the solution to describe exterior fields of neutron stars, we present an extensive comparison of the radii of innermost stable circular orbits (ISCOs) obtained from Berti & Stergioulas numerical solutions, Kerr solution (Phys. Rev. Lett. 11, 237 (1963)), Hartle & Thorne solution (Ap. J. 153, 807, (1968)), an analytic series expansion derived by Shibata & Sasaki (Phys. Rev. D. 58 104011 (1998)) and, our exact solution. We found that radii of ISCOs from our solution fits better than others with realistic numerical interior solutions.