Newtonian View of General Relativistic Stars

Abstract

Although general relativistic cosmological solutions, even in the presence of pressure, can be mimicked by using neo-Newtonian hydrodynamics, it is not clear whether there exists the same Newtonian correspondence for spherical static configurations. General relativity solutions for stars are known as the Tolman-Oppenheimer-Volkoff (TOV) equations. On the other hand, the Newtonian description does not take into account the total pressure effects and therefore can not be used in strong field regimes. We discuss how to incorporate pressure in the stellar equilibrium equations within the neo-Newtonian framework. We compare the Newtonian, neo-Newtonian and the full relativistic theory by solving the equilibrium equations for both three approaches and calculating the mass-radius diagrams for some simple neutron stars equation of state.

arXiv comment6 pages, 3 figures. v2 matches accepted version (EPJC)

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• On stability of a neutron star system in Palatini gravity
• Polytropic stars in Palatini gravity
• Analogue Aharonov-Bohm effect in neo-Newtonian theory
• Dilatonic Equation of Hydrostatic Equilibrium and Neutron Star Structure
• Neutron stars in Einstein-$\Lambda$ gravity: the cosmological constant effects
• Contraction of cold neutron star due to in the presence a quark core
• Thin-Shell Wormholes in Neo-Newtonian Theory
• Properties of white dwarfs in Einstein-$\Lambda$ gravity
• The Palatini star: exact solutions of the modified Lane-Emden equation
• A Generalized Double Chaplygin Model for Anisotropic Matter: The Newtonian Case
• Properties of Neutron Stars with hyperon cores in parameterized hydrostatic conditions
• The structure of hybrid neutron star in Einstein-$\Lambda$ gravity
• Aharonov-Bohm effect for a fermion field in a planar black hole "spacetime"