**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.;