Newtonian hydrodynamics with general relativistic pressure

Abstract

We present the general relativistic pressure correction terms in Newtonian hydrodynamic equations to the nonlinear order: these are equations (1)-(3). The derivation is made in the zero-shear gauge based on the fully nonlinear formulation of cosmological perturbation in Einstein's gravity. The correction terms differ from many of the previously suggested forms in the literature based on hand-waving manners. We confirm our results by comparing with (i) the nonlinear perturbation theory, (ii) the first order post-Newtonian approximation, and (iii) the special relativistic limit, and by checking (iv) the consistency with full Einstein's equation.

Newtonian cosmology with a quantum bounce

“…Indeed, it has been addressed in a number of papers [33][34][35][36][37][38] without invoking theh-correction present in our Friedmann equations. The adequate theory of cosmological perturbations consistent with general relativity requires a set up which goes beyond the Newtonian approach presented in this paper even in the caseh → 0.…”

Fully non-linear cosmological perturbations of multicomponent fluid and field systems

“…where the second term is missing in the right-hand-side of the same equation; the form of missing term varies depending on the way of derivation. In Hwang & Noh (2013c) we have attributed this failure as due to the higher order (in c −2 ) nature of equation (62). Accepting this argument we have checked the consistency of all the Einstein's equations.…”

“…The formulation ignores spatially transverse-tracefree (tensor-type) perturbation, but have not taken the slicing (temporal gauge) condition. Besides simple derivation of the perturbation equations to any nonlinear order, the formulation was used to show the Newtonian limit, the first-order post-Newtonian approximation and the Newtonian hydrodynamic equations with general relativistic (gravitating) pressure (Hwang & Noh 2013b, 2013c, Noh & Hwang 2013. The formulation considered a fluid (without anisotropic stress) or a scalar field system.…”

Newtonian hydrodynamic equations with relativistic pressure and velocity

“…(7). We present the energy conservation, momentum conservation and Poisson's equation which allow us to handle such astrophysical situations in Newtonian manner.…”

“…Here, we provide a complementary approximation which can handle the fully relativistic pressure and velocity in the weak gravity and action-at-a-distance limit: for our assumptions see Eq. (7). We present the energy conservation, momentum conservation and Poisson's equation which allow us to handle such astrophysical situations in Newtonian manner.…”