Anisotropic Geodesic Fluid Spheres in General Relativity

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. Postal address: Apartado 80793, Caracas 1080 A, Venezuela; e-mail address: [email protected] e-mail address:[email protected]