paper

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

arXiv:1506.06050 · doi:10.1103/PhysRevD.92.124030

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 , the mass quadrupole moment , and the tidal Love number in exact form. The -- 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.

10 pages, 2 figures, v2: various improvements, to appear in PRD, v3: erratum available as an ancillary file and at https://www.dropbox.com/s/0d1gsgy0idqtihi/erratum_1506.06050.pdf?dl=0 correcting the final result for the moment of inertia and for the tidal Love number

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