1. A Note on Incompressibility of Relativistic Fluids and the Instantaneity of their Pressures
- Author
-
Moritz Reintjes
- Subjects
Spacetime ,010102 general mathematics ,FOS: Physical sciences ,Statistical and Nonlinear Physics ,General Relativity and Quantum Cosmology (gr-qc) ,Relativistic Euler equations ,01 natural sciences ,General Relativity and Quantum Cosmology ,Classical limit ,010305 fluids & plasmas ,Euler equations ,Physics::Fluid Dynamics ,symbols.namesake ,Elliptic curve ,Theory of relativity ,83C99 (Primary), 76B99 (Secondary) ,0103 physical sciences ,symbols ,Compressibility ,Incompressible euler equations ,0101 mathematics ,Mathematical Physics ,Mathematics ,Mathematical physics - Abstract
We introduce a natural notion of incompressibility for fluids governed by the relativistic Euler equations on a fixed background spacetime, and show that the resulting equations reduce to the incompressible Euler equations in the classical limit as $c\rightarrow \infty$. As our main result, we prove that the fluid pressure of solutions of these incompressible "relativistic" Euler equations satisfies an elliptic equation on each of the hypersurfaces orthogonal to the fluid four-velocity, which indicates infinite speed of propagation., Comment: 7 pages. Version 2: Improved wording and presentation
- Published
- 2018
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