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Abstract

We investigate spherically symmetric cosmological models in Einstein-aether
theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame
formalism and adopt the comoving aether gauge to derive the evolution
equations, which form a well-posed system of first order partial differential
equations in two variables. We then introduce normalized variables. The
formalism is particularly well-suited for numerical computations and the study
of the qualitative properties of the models, which are also solutions of Horava
gravity. We study the local stability of the equilibrium points of the
resulting dynamical system corresponding to physically realistic inhomogeneous
cosmological models and astrophysical objects with values for the parameters
which are consistent with current constraints. In particular, we consider dust
models in ($\beta-$) normalized variables and derive a reduced (closed)
evolution system and we obtain the general evolution equations for the
spatially homogeneous Kantowski-Sachs models using appropriate bounded
normalized variables. We then analyse these models, with special emphasis on
the future asymptotic behaviour for different values of the parameters.
Finally, we investigate static models for a mixture of a (necessarily
non-tilted) perfect fluid with a barotropic equations of state and a scalar
field.