Abstract
We implement the so-called “complex-plane strategy” for computing general-relativistic polytropic models of uniformly rotating neutron stars. This method manages the problem by performing all numerical integrations, required within the framework of Hartle’s perturbation method, in the complex plane. We give emphasis on computing corrections up to third order in the angular velocity, and the mass-shedding limit. We also compute the angular momentum, moment of inertia, rotational kinetic energy, and gravitational potential energy of the models considered.
Highlights
We implement the so-called “complex-plane strategy” for computing general-relativistic polytropic models of uniformly rotating neutron stars. This method manages the problem by performing all numerical integrations, required within the framework of Hartle’s perturbation method, in the complex plane
In a recent paper [1], we have applied the so-called “complex-plane strategy” (CPS), originally developed and used for computing classical polytropic models in rapid rotation, to compute rapidly rotating neutron stars simulated by general-relativistic polytropic models, i.e. neutron stars obeying the well-known polytropic “equation of state” (EOS) (see e.g. [1], Section 2.1, Equations (5)-(9))
We implement Hartle’s perturbation method ([4,5,6]) in order to compute 1) the structure of a rotating neutron star up to terms of third order in the angular velocity, and 2) the mass-shedding limit, i.e. the angular velocity above which the gravitational attraction, compared to the centrifugal force, is not sufficient to keep matter bound to the surface ([7], Section 6.5.2; [8], Section 5.2.2; [9], Section 5)
Summary
In a recent paper [1], we have applied the so-called “complex-plane strategy” (CPS), originally developed and used for computing classical polytropic models in rapid rotation (see e.g. [2,3]), to compute rapidly rotating neutron stars simulated by general-relativistic polytropic models, i.e. neutron stars obeying the well-known polytropic “equation of state” (EOS) (see e.g. [1], Section 2.1, Equations (5)-(9)). We implement Hartle’s perturbation method ([4,5,6]) in order to compute 1) the structure of a rotating neutron star up to terms of third order in the angular velocity , and 2) the mass-shedding limit, i.e. the angular velocity above which the gravitational attraction, compared to the centrifugal force, is not sufficient to keep matter bound to the surface ([7], Section 6.5.2; [8], Section 5.2.2; [9], Section 5). The function w3 affects the massshedding velocity and, the mass-shedding limit ([10], Section 2A; see [11], Section 3). Both w1 and w3 contribute to the dragging of the inertial frames. The physical quantities involved in this study are expressed in gravitational units (see e.g. [1], Section 1.2)
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