Approximate mass and radius formulas for static and rotating strange stars

Abstract

Using the general relativistic conditions of thermodynamic equilibrium and fitting with values obtained from numerical integration of structure equations we derive approximate mass and radius formulas for static and uniformly rotating strange stars obeying the bag model equation of state. In the static case our formulas can reproduce the values of the mass and radius of the quark star with an error smaller than 1%. The maximum mass and radius of the strange stars can be predicted by fitting only one set of static configuration data. With the use of results obtained for the static configuration and with some supplementary assumptions about the behavior of the metric tensor at the center of the star, we can predict the rotational properties of maximally rotating strange stars within an error of 3%. From the approximate formulas we can derive the "empirical" formula relating the maximum rotation frequency of the uniformly rotating strange stars to the mass and radius of the maximum allowable static configuration. ©2000 The American Physical Society.