I-Love-Q relations for a gravastar and the approach to the black-hole limit

TL;DR

This paper investigates the properties of gravastars, hypothetical compact objects, and their relations to black holes, revealing that while they differ from ordinary stars, they approach black-hole characteristics in the maximum compactness limit.

Contribution

It provides exact calculations of multipole moments and tidal Love numbers for gravastars and explores their relations to black-hole limits, highlighting differences from ordinary stars.

Findings

Gravastar relations differ significantly from ordinary stars.

The black-hole limit for gravastars is continuous and approaches Kerr black hole values.

The approach to the black-hole limit is nonpolynomial, unlike neutron stars.

Abstract

The multipole moments and the tidal Love numbers of neutron stars and quark stars satisfy certain relations which are almost insensitive to the star's internal structure. A natural question is whether the same relations hold for different compact objects and how they possibly approach the black-hole limit. Here we consider "gravastars", which are hypothetical compact objects sustained by their internal vacuum energy. Such solutions have been proposed as exotic alternatives to the black-hole paradigm because they can be as compact as black holes and exist in any mass range. By constructing slowly-rotating, thin-shell gravastars to quadratic order in the spin, we compute the moment of inertia $I$, the mass quadrupole moment $Q$, and the tidal Love number $\lambda$ in exact form. The $I$-$\lambda$-$Q$ relations of a gravastar are dramatically different from those of an ordinary compact star, but the black-hole limit is continuous, i.e. these quantities approach their Kerr counterparts when the compactness is maximum. Therefore, such relations can be used to discern a gravastar from an ordinary compact star, but not to break the degeneracy with the black-hole case. Based on these results, we conjecture that the full multipolar structure and the tidal deformability of a spinning, ultracompact gravastar are identical to those of a Kerr black hole. The approach to the black-hole limit is nonpolynomial, thus differing from the critical behavior recently found for strongly anisotropic neutron stars.