Newtonian View of General Relativistic Stars

TL;DR

This paper explores how to incorporate pressure effects into neo-Newtonian models of static stars and compares these models with full relativistic solutions to understand their accuracy in strong gravity regimes.

Contribution

It introduces a method to include pressure in neo-Newtonian stellar models and compares these with relativistic solutions for neutron stars.

Findings

Neo-Newtonian models better approximate relativistic solutions when pressure effects are included.

Mass-radius diagrams show improved agreement between neo-Newtonian and relativistic models.

Relativistic effects become significant in strong gravity regimes, limiting neo-Newtonian applicability.

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.