Abstract
In this paper we study anisotropic spherical polytropes within the framework of general relativity. Using the anisotropic Tolman-Oppenheimer-Volkov (TOV) equations, we explore the relativistic anisotropic Lane-Emden equations. We find how the anisotropic pressure affects the boundary conditions of these equations. Also we argue that the behaviour of physical quantities near the center of star changes in the presence of anisotropy. For constant density, a class of exact solution is derived with the aid of a new ansatz and its physical properties are discussed.
Highlights
In theoretical astrophysics there is a growing interest to discuss the stellar structures in which the matter content is an anisotropic fluid
The effect of anisotropy can be studied both in Newtonian gravity and general relativity
For the configurations with not extremely high densities, the presence of an anisotropy factor has been discussed in the Newtonian regime [1,2,3] and otherwise general relativity must be used
Summary
In theoretical astrophysics there is a growing interest to discuss the stellar structures in which the matter content is an anisotropic fluid. Our main purpose is to obtain the exact solutions of general relativistic star equations in the presence of anisotropic pressure. We derive the relativistic Lane–Emden equations in the presence of anisotropy factor We obtain their boundary conditions and generalize the Chandrasekhar’s theorem [45] to the anisotropic case. In order to obtain the exact solutions, we have assumed that the presence of anisotropy factor does not change the general form of the relativistic hydrostatic equilibrium equations. This ansatz leads us to find a new class of exact solutions for the anisotropic Lane–Emden equations for constant density.
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