We study the anisotropic self-gravitating objects with polytropic equation of state in both contexts of Newtonian gravity and General Relativity.
First we discuss Newtonian case, where we start with hydrostatic equilibrium equation. By arriving at Lane--Emden equation we study the effects of an anisotropic pressure on the boundary conditions of the anisotropic Lane–Emden equation and the homology theorem.
Then we go to the relativistic case and by using the anisotropic Tolman–Oppenheimer–Volkov (TOV) equations, we explore the relativistic anisotropic Lane–Emden equations. After that we find how the anisotropic pressure affects the boundary conditions of these equations.
For both cases some new physically well-defined solutions are derived.
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