Regular Article – Theoretical Physics
Einstein–æther models III: conformally static metrics, perfect fluid and scalar fields
Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta, Chile
2 Department of Mathematics and Statistics, Dalhousie University, B3H 3J5, Halifax, NS, Canada
Accepted: 3 December 2020
Published online: 24 December 2020
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 . To analyze locally the behavior of the solutions near a sonic line , 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 . 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 with potential the symmetry of the conformally static metric restrict the scalar fields to be considered to , . An exhaustive analysis (analytical or numerical) of the stability conditions is provided for some particular cases.
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