  We present a general relativistic version of the self-gravitating fluid model
for the dark sector of the Universe (darkon fluid) introduced in Phys. Rev. 80
(2009) 083513 and extended and reviewed in Entropy (2013) 559. This model
contains no free parameters in its Lagrangian. The resulting energy-momentum
tensor is dustlike with a nontrivial energy-flow. In an approximation valid at
sub-Hubble scales we find that the cosmic acceleration is not attributed to any
kind of negative pressure but it is due to a dynamically determined sign change
of the energy density. This property turns out to be equivalent to a
time-dependent, sign changing curvature. The cosmological equations obtained
agree with those of the nonrelativistic model but they are given a new physical
interpretation. Furthermore we have derived the self-consistent equation to be
satisfied by the nonrelativistic gravitational potential produced by a galactic
halo in our model from a weak field limit of a generalized
Tolman-Oppenheimer-Volkoff equation.
