Editor's Note: Relativistic Hydrodynamics

Abstract

The general theory of relativity may be viewed as the completion of classical macroscopic field physics. Since this theory identifies gravitation with some aspects of the metric of spacetime, and because the metric and its connection enter all parts of physics as basic prerequisites, the task arose to adapt all branches of classical physics to the generalized spacetime structure, and to investigate whether the modifications lead to new, possibly observable consequences. This holds, in particular, for hydrodynamics, the significance of which in this context is enhanced by the following facts. Due to an elementary argument by Max von Laue [1], relativistic causality implies that any extended body has infinitely many degrees of freedom, and the results of Karl Schwarzschild [2] and of subsequent authors show that Einstein’s gravitational field equation is incompatible with the representation of bodies as points endowed with a positive mass. Therefore, in general relativity bodies such as stars and planets have to be modelled, at least in principle, in terms of hydroor elastomechanics. In addition, the development of high-energy astrophysics shows that large-scale flows of matter with relativistic speeds in relativistic gravitational fields do occur in nature. Prime examples are supernovae, jets associated with active galactic nuclei, accretion flows