  The equations of state for a characteristic spacetime are studied in the
context of the spherically symmetric interior exact and analytical solutions in
Horava gravity and Einstein-aether theory in which anisotropic fluids are
considered. In particular, for a given anisotropic interior solution, the
equations of state relating the density to the radial and tangential pressure
are derived, by means of a polynomial best-fit. Moreover, the well-known
relativistic polytropic equations of state are used in order to obtain the
profile of the thermodynamical quantities inside the stellar object as provided
by the specific exact solution considered. It is then shown that these
equations of state need to be modified in order to account for the profiles of
density and pressures.
