Special relativistic hydrodynamics with gravitation

Abstract

The special relativistic hydrodynamics with weak gravity is hitherto unknown in the literature. Whether such an asymmetric combination is possible was unclear. Here, the hydrodynamic equations with Poisson-type gravity considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit are consistently derived from Einstein's general relativity. Analysis is made in the maximal slicing where the Poisson's equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the {\it general} hypersurface condition. Our formulation includes the anisotropic stress.

arXiv comment15 pages, no figure. Accepted in ApJ

References in corpus (13)

• Second-order Perturbations of the Friedmann World Model
• From Lorenz to Coulomb and other explicit gauge transformations
• Equation of State in Numerical Relativistic Hydrodynamics
• Cosmological nonlinear hydrodynamics with post-Newtonian corrections
• Post-Newtonian Hydrodynamic Equations Using the (3+1) Formalism in General Relativity
• Fully nonlinear and exact perturbations of the Friedmann world model
• Post-Newtonian Approximation
• Newtonian limit of fully nonlinear cosmological perturbations in Einstein's gravity
• Post-Newtonian Lagrangian Perturbation Approach to the Large-Scale Structure Formation
• Fully nonlinear and exact perturbations of the Friedmann world model: Non-flat background
• Newtonian Hydrodynamics with General Relativistic Pressure
• Cosmological post-Newtonian equations from nonlinear perturbation theory
• Newtonian hydrodynamic equations with relativistic pressure and velocity

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