Application of the improved Hartle method for the construction of general relativistic rotating neutron star models

Abstract

Models of general relativistic rotating neutron stars, constructed from Hartle's (1967) perturbative 'slow' rotation formalism of massive relativistic objects, are compared with their counterparts obtained from the exact solution of Einstein's equations. It is found that both methods, perturbative and exact, lead to compatible results down to rotational Kepler periods P(K) of about 0.5 ms, a value which is by far smaller than the smallest yet observed pulsar period. This finding rests on the reinvestigation of Hartle's method, supplementing it by a self-consistency condition inherent in the determination of the Kepler frequency, and analyzing carefully sequences of star models near their end points. A collection of 17 representative neutron matter equations of state served as an input. Because of its simple structure, Hartle's method should prove to be a practical tool for testing models of the nuclear equation of state with data on pulsar periods. The form of an approximate empirical formula for the general relativistic Kepler frequency is obtained, and proportionality to the Newtonian expression arises in about equal parts from the equatorial flattening and the frame dragging.