Abstract

The asymptotic properties of conformally static metrics in Einstein–æther theory with a perfect fluid source and a scalar field are analyzed. In case of perfect fluid, some relativistic solutions are recovered such as: Minkowski spacetime, the Kasner solution, a flat FLRW space and static orbits depending on the barotropic parameter γ. To analyze locally the behavior of the solutions near a sonic line v2= γ- 1 , where v is the tilt, a new “shock” variable is used. Two new equilibrium points on this line are found. These points do not exist in General Relativity when 1 < γ< 2. In the limiting case of General Relativity these points represent stiff solutions with extreme tilt. Lines of equilibrium points associated with a change of causality of the homothetic vector field are found in the limit of general relativity. For non-homogeneous scalar field ϕ(t, x) with potential V(ϕ(t, x)) the symmetry of the conformally static metric restrict the scalar fields to be considered to ϕ(t, x) = ψ(x) - λt, V(ϕ(t, x)) = e-2tU(ψ(x)) , U(ψ)=U0e-2ψλ. An exhaustive analysis (analytical or numerical) of the stability conditions is provided for some particular cases.