Exact Anisotropic Solutions of the Generalized TOV Equation
Nematollah Riazi, S. Sedigheh Hashemi, S. Naseh Sajadi, S. Shahrokh, Assyaee
TL;DR
This paper derives exact solutions for anisotropic relativistic spheres using a generalized TOV equation with a bi-polytropic equation of state, analyzing their properties and stability.
Contribution
It introduces a new class of exact anisotropic solutions to the generalized TOV equation with a bi-polytropic EoS, including stability and horizon conditions.
Findings
Solutions are regular at the origin and asymptotically flat.
Conditions for horizon formation are identified.
Basic stability analysis is provided.
Abstract
We explore gravitating relativistic spheres composed of an anisotropic, barotropic uid. We assume a bi-polytropic equation of state which has a linear and a power-law terms. The generalized Tolman-Oppenheimer-Volkoff (TOV) equation which describes the hydrostatic equilibrium is obtained. The full system of equations are solved for solutions which are regular at the origin and asymptotically flat. Conditions for the appearance of horizon and a basic treatment of stability are also discussed.
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