On the construction of relativistic hydrodynamic equations in curved space-time written in abstract geometrical notations

Abstract

This paper presents a macroscopic derivation of the system of equations of relativistic dissipative hydrodynamics in an abstract geometrical form, which does not depend on the chosen space-time coordinates and reduces to equations valid in both flat and curved space-time. The above procedure, serving as a link between the non-gravitational laws of physics and gravitation, is based on Einstein's equivalence principle which guarantees that the laws of physics written in abstract geometrical representation have the same form both in flat and curved spacetime. A modern formulation of relativistic hydrodynamics based on both classical nonequilibrium thermodynamics (first-order theory) and expanded irreversible thermodynamics (second-order theory) is proposed. The theory presented has both purely conceptual and applied significance. In particular, this theory has applications in such important fields of knowledge as nuclear physics, astrophysics and cosmology. For example, in viscous cosmological models, bulk viscosity acts as a cause of dissipation, which has a significant impact on the processes in the Universe.