The Energy-Momentum Tensor for a Dissipative Fluid in General Relativity

TL;DR

This paper analyzes the energy-momentum tensor of a viscous, dissipative fluid in general relativity, relating stresses to viscosity and spacetime symmetries, and evaluates energy conditions without restrictive assumptions.

Contribution

It introduces a general form of the energy-momentum tensor for dissipative fluids and links stresses to extrinsic curvature and spacetime symmetries, providing a new approach to energy condition analysis.

Findings

Derived relations between stresses and viscosity coefficients.

Connected stresses with extrinsic curvature of the normal surface.

Calculated energy conditions without restrictive assumptions.

Abstract

Considering the growing interest of the astrophysicist community in the study of dissipative fluids with the aim of getting a more realistic description of the universe, we present in this paper a physical analysis of the energy-momentum tensor of a viscous fluid with heat flux. We introduce the general form of this tensor and, using the approximation of small velocity gradients, we relate the stresses of the fluid with the viscosity coefficients, the shear tensor and the expansion factor. Exploiting these relations, we can write the stresses in terms of the extrinsic curvature of the normal surface to the 4-velocity vector of the fluid, and we can also establish a connection between the perfect fluid and the symmetries of the spacetime. On the other hand, we calculate the energy conditions for a dissipative fluid through contractions of the energy-momentum tensor with the 4-velocity vector of an arbitrary observer. This method is interesting because it allows us to compute the conditions in a reasonable easy way and without considering any approximation or restriction on the energy-momentum tensor.