Hierarchy of Universal Relations for Neutron Stars in Terms of Multipole Moments

TL;DR

This paper explores a hierarchy of universal relations for neutron stars based on multipole moments, revealing that some conjectures about their properties may not hold for perfect fluid models but could for anisotropic ones.

Contribution

It introduces an infinite hierarchy of universal relations for neutron stars derived from soliton solutions of Einstein's equations.

Findings

Universal relations form an infinite hierarchy based on multipole moments.

The no-hair conjecture fails for perfect fluid neutron star models.

The conjecture might still hold for models with anisotropic fluid.

Abstract

Recent studies of the analytical and numerical models of neutron stars suggest that their exterior field can be described by only four arbitrary parameters of the 2-soliton solution of Einstein's equations. Assuming that this is the case, we show that there exists an infinite hierarchy of the universal relations for neutron stars in terms of multipole moments that arises as a series of the degeneration conditions for generic soliton solutions. Our analysis of the simplest of these relations shows that the no-hair conjecture for neutron stars proposed by Yagi {\it et al.} fails to be verified by the perfect fluid models, but we argue that the conjecture could still be true for the models involving anisotropic fluid.