Newtonian View of General Relativistic Stars

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.Comment: 6 pages, 3 figures. v2 matches accepted version (EPJC

A note on acoustic black holes in neo-Newtonian theory

Newtonian fluid dynamics allows the construction of acoustic metrics from which black hole configurations can be studied. However, relativistic pressure effects are neglected within Newtonian theory. We study acoustic black holes in the framework of neo-Newtonian hydrodynamics, which is designed to take into account relativistic inertial effects of the pressure $p$. Within this new hydrodynamical context we show how $p$ can influence the formation of the acoustic horizons.Comment: Latex file, 10 pages. Some discussions extended. Accepted for publication in MPL