Eur. Phys. J. C (2014) 74: 3170
https://doi.org/10.1140/epjc/s10052-014-3170-2

Regular Article - Theoretical Physics

Newtonian view of general relativistic stars

¹ Grupo de Ciências Ambientais e Recursos Naturais, Instituto Federal do Espírito Santo (IFES), Guarapari, Brazil
² Departamento de Física, Universidade Federal do Espírito Santo (UFES), Vitória, Brazil
³ Institut de Mathématiques et de Sciences Physiques (IMSP), Porto-Novo, Bénin

^* e-mail: velten@pq.cnpq.br

Received: 1 October 2014
Accepted: 5 November 2014
Published online: 26 November 2014

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 cannot 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’ equations of state.