Quasi-radial modes of pulsating neutron stars: numerical results for general-relativistic rigidly rotating polytropic models

In this paper we compute general-relativistic polytropic models simulating rigidly rotating, pulsating neutron stars. These relativistic compact objects, with a radius of $\sim 10 \, \mathrm{km}$ and mass between $\sim 1.4$ and $3.2$ solar masses, are closely related to pulsars. We emphasize on computing the change in the pulsation eigenfrequencies owing to a rigid rotation, which, in turn, is a decisive issue for studying stability of such objects. In our computations, we keep rotational perturbation terms of up to second order in the angular velocity.Comment: v1 has been submitted to the International Journal of Astronomy and Astrophysics and accepted after revision; v2, i.e. the present version, is the revised E-print; 16 page

Radial pulsations of neutron stars: computing alternative polytropic models regarding density and adiabatic index

We revisit the problem of radial pulsations of neutron stars by computing four general-relativistic polytropic models, in which "density" and "adiabatic index" are involved with their discrete meanings: (i) "rest-mass density" or (ii) "mass-energy density" regarding the density, and (i) "constant" or (ii) "variable" regarding the adiabatic index. Considering the resulting four discrete combinations, we construct corresponding models and compute for each model the frequencies of the lowest three radial modes. Comparisons with previous results are made. The deviations of respective frequencies of the resolved models seem to exhibit a systematic behavior, an issue discussed here in detail.Comment: 19 page

Explicit Inversion for Two Brownian-Type Matrices

We present explicit inverses of two Brownian--type matrices, which are defined as Hadamard products of certain already known matrices. The matrices under consideration are defined by $3n-1$ parameters and their lower Hessenberg form inverses are expressed analytically in terms of these parameters. Such matrices are useful in the theory of digital signal processing and in testing matrix inversion algorithms.Comment: v3 has been submitted to Applied Mathematics (http://www.SciRP.org/journal/am) and accepted after revision; v4, i.e. the present version, is the revised E-print (title modified; some remarks and Eqs. (6)-(7) added in Sec. 1; Secs. 2 and 3 reformed; Sec. 5 added; References [6]-[7] added); 10 page

Critical rotation of general-relativistic polytropic models simulating neutron stars: a post-Newtonian hybrid approximative scheme

We develop a "hybrid approximative scheme" in the framework of the post-Newtonian approximation for computing general-relativistic polytropic models simulating neutron stars in critical rigid rotation. We treat the differential equations governing such a model as a "complex initial value problem", and we solve it by using the so-called "complex-plane strategy". We incorporate into the computations the complete solution for the relativistic effects, this issue representing a significant improvement with regard to the classical post-Newtonian approximation, as verified by extended comparisons of the numerical results.Comment: 24 page