Relativistic hydrodynamics: the representation of several fluids in general relativity

The energy-momentum tensor is the mathematical entity that represents the sources of momentum and energy in a covariant formalism, both in flat and curved spaces. In curved spaces the energy-momentum tensor is connected tBo the space-time curvature via the Einstein field equation. The energy-momentum tensor characterizes the matter fields of the system. In turn, the energy conditions established by Hawking and Ellis classify the various types of fluids according to their attractiveness/repulsiveness, causality, interaction with the vacuum and positivity. We also address the conservation of the energy-momentum tensor via the Tolemam-Openhaimer-Volkov (TOV) equation, which is an important formalism for the study of stellar structures and models. We will study the energy-momentum tensor in its isotropic and anisotropic versions, as well as its conservation and relation to the cosmological constant.

Keywords:
Hydrodynamics; Relativistic Fluids