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Spherically symmetric relativistic stars with the polytropic equation ofstate, which possess the local pressure anisotropy, are considered in thecontext of general relativity. The modified Lane-Emden equations are derivedfor the special ansatz for the anisotropy parameter $\Delta$ in the form of thedifferential relation between $\Delta$ and the metric function $\nu$. Theanalytical solutions of the obtained equations are found for incompressiblefluid stars. The dynamical stability of incompressible anisotropic fluid starsagainst radial oscillations is studied.

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