Anisotropic geodesic fluid spheres in general relativity

TL;DR

This paper explores anisotropic fluid spheres in general relativity, showing they can be geodesic without zero pressure gradients, leading to dynamic models with explicit solutions.

Contribution

It introduces models of anisotropic fluids that are geodesic without requiring vanishing pressure gradients, extending previous perfect fluid results.

Findings

Anisotropic fluids can be geodesic without zero pressure gradients.

Derived explicit models with dynamic behavior.

Expressed mass function in terms of local fluid velocity.

Abstract

It is shown that unlike the perfect fluid case, anisotropic fluids (principal stresses unequal) may be geodesic, without this implying the vanishing of (spatial) pressure gradients. Then the condition of vanishing four acceleration is integrated in non-comoving coordinates. The resulting models are necessarily dynamic, and the mass function is expressed in terms of the fluid velocity as measured by a locally Minkowskian observer. An explicit example is worked out.