**Publication date:** Aug 2013

**Abstract:**

We present results for models of neutron stars and strange stars constructed using the Hartle-Thorne slow-rotation method with a wide range of equations of state, focusing on the values obtained for the angular momentum J and the quadrupole moment Q, when the gravitational mass M and the rotational frequency Ω are specified. Building on previous work, which showed surprising uniformity in the behaviour of the moment of inertia for neutron-star models constructed with widely different equations of state, we find similar uniformity for the quadrupole moment. These two quantities, together with the mass, are fundamental for determining the vacuum space-time outside neutron stars. We study particularly the dimensionless combination of parameters QM/J^{2} (using units for which c = G = 1). This quantity goes to 1 in the case of a Kerr-metric black hole and deviations away from 1 then characterize the difference between neutron-star and black hole space-time. It is found that QM/J^{2} for both neutron stars and strange stars decreases with increasing mass, for a given equation of state, reaching a value of around 2 (or even less) for maximum-mass models, meaning that their external space-time is then not very far from that of the Kerr metric. If QM/J^{2} is plotted against R/2M (where R is the radius), it is found that the relationship is nearly unique for neutron-star models, independent of the equation of state, while it is significantly different for strange stars. This gives a new way of possibly distinguishing between them.

**Authors:**

Urbanec, M.; Miller, J. C.; Stuchlík, Z.;