  We start with a recently introduced spherically symmetric geodesic fluid
model (arXiv: 1601.07030) whose energy-momentum tensor 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.
