Relativistic anisotropic stars with the polytropic equation of state in general relativity

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 $\Delta$ in the form of the differential relation between $\Delta$ and the metric function $\nu$. 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.

V1: 6 pages, 1 table. Compared to arXiv:1801.03745, a different set of the trial functions and values of the anisotropy coefficient $\beta$ is used in the variational procedure. V2: Added acknowledgement

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