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arXiv · 1309.7680

Newtonian Hydrodynamics with General Relativistic Pressure

Jai-chan Hwang·Hyerim Noh
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Abstract

We present the general relativistic pressure correction terms in Newtonian hydrodynamic equations to the nonlinear order: these are equations (\ref{mass-conservation-Mink})-(\ref{Poisson-eq-Mink}). 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 {\it 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.

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Jai-chan Hwang, Hyerim Noh. 2013-09-30. Newtonian Hydrodynamics with General Relativistic Pressure. https://doi.org/10.1088/1475-7516%2F2013%2F10%2F054

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