Cosmology and stellar equilibrium using Newtonian hydrodynamics with general relativistic pressure

TL;DR

This paper derives Newtonian equations incorporating relativistic pressure effects, analyzing their impact on cosmology and stellar equilibrium, revealing significant differences from standard theories and potential for improved simulations.

Contribution

The authors explicitly derive and analyze Newtonian equations with relativistic pressure effects, comparing their predictions with General Relativity and other theories in cosmology and stellar physics.

Findings

Universe acceleration with positive pressure predicted

Small-scale perturbations match relativistic results

Neutron star mass limits are significantly higher

Abstract

We revisit the analysis made by Hwang and Noh [JCAP 1310 (2013)] aiming the construction of a Newtonian set of equations incorporating pressure effects typical of the General Relativity theory. We explicitly derive the Hwang-Noh equations, comparing them with similar computations found in the literature. Then, we investigate $i)$ the cosmological expansion, $ii)$ linear cosmological perturbations theory and $iii)$ stellar equilibrium by using the new set of equations and comparing the results with those coming from the usual Newtonian theory, from the Neo-Newtonian theory and from the General Relativity theory. We show that the predictions for the background evolution of the Universe are deeply changed with respect to the General Relativity theory: the acceleration of the Universe is achieved with positive pressure. On the other hand, the behaviour of small cosmological perturbations reproduces the one found in the relativistic context, even if only at small scales. We argue that this last result may open new possibilities for numerical simulations for structure formation in the Universe. Finally, the properties of neutron stars are qualitatively reproduced by Hwang-Noh equations, but the upper mass limit is at least one order of magnitude higher than the one obtained in General Relativity.