Anisotropic Geodesic Fluid in Non-Comoving Spherical Coordinates

Abstract

We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving energy frame (vanishing energy flux), the same EMT contains besides dust only radial pressure. We present Einstein’s equations together with the matter equations in static spherically symmetric coordinates. These equations are self-contained (four equations for four unknowns). We solve them analytically except for a resulting nonlinear ordinary differential equation (ODE) for the gravitational potential. This ODE can be rewritten as a Lienard differential equation which, however, may be transformed into a rational Abel differential equation of the first kind. Finally, we list some open mathematical problems and outline possible physical applications (galactic halos, dark energy stars) and related open problems.