Inhomogeneous spacetimes in Einstein-\ae ther Cosmology

We investigate the existence of inhomogeneous Szekeres spacetimes in Einstein-\ae ther theory. We show that inhomogeneous solutions which can be seen as extension of the Szekeres solutions existing in Einstein-\ae ther gravity only for a specific relation between the dimensionless coefficients which defines the coupling between the \ae ther filed with gravity. The two Szekeres classes of solutions are derived. Also a class of inhomogeneous FLRW-like spacetimes is allowed by the theory for arbitrary values of the dimensionless coefficients of the \ae ther field. The stability of the solutions obtained is performed from where we find that the field equations evolve more variously in Einstein-\ae ther than in General Relativity, where isotropic spacetimes and Kantowski-Sachs spacetimes are found to be attractors.