Abstract
Spherically symmetric relativistic stars with the polytropic equation of state, which possess the local pressure anisotropy, are considered in the context of general relativity. The modified Lane-Emden equations are derived for the special ansatz for the anisotropy parameter Δ in the form of the differential relation between Δ and the metric function ν. The analytical solutions of the obtained equations are found for incompressible fluid stars. The dynamical stability of incompressible anisotropic fluid stars against radial oscillations is studied.
Highlights
Basic equations It was suggested in Ref. [1] that, despite the spherically symmetric distribution of matter inside a compact stellar object, it can be characterized by the local pressure anisotropy
We apply the Chandrasekhar variational procedure [13] to study the dynamical stability of incompressible anisotropic fluid stars with respect to radial oscillations
(3), one can get in the static limit the equation for the hydrostatic equilibrium in the presence of the pressure anisotropy in the form pr′
Summary
Basic equations It was suggested in Ref. [1] that, despite the spherically symmetric distribution of matter inside a compact stellar object, it can be characterized by the local pressure anisotropy. We will study spherical relativistic anisotropic stars with the polytropic equation of state, aiming to obtain the modified Lane-Emden (LE) equations for the special ansatz for the anisotropy parameter ∆ in the form of the differential relation between ∆ and the metric function ν. The obtained LE equations can be integrated only numerically, but the analytic solutions can be found for incompressible fluid stars.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
