  The space of the solutions of the differential equations resulting from
considering matter fluids of scalar field type or perfect fluid in
Einstein-aether theory is analyzed. The Einstein-aether theory of gravity
consists of General Relativity coupled to a vector field of unit time type,
called the aether. In this effective theory, Lorentz invariance is violated,
but locality and covariance are preserved in the presence of the vector field.
For the mathematical formulation of the models, the 1 + 3 formalism is used
that allows writing field equations for spherically symmetric inhomogeneous
metrics as a system of partial differential equations in two variables. Using
the homothetic diagonal formulation, the Partial differential equations can be
written as ordinary differential equations plus algebraic constraints, using
the fact that the metric adapts to homothetic symmetry. The resulting equations
are very similar to those of the models with homogeneous hypersurfaces. This
allows the qualitative study of the solutions using techniques of local theory
of dynamic systems. Analytical results are verified numerically.
