Some 3-dimensional Maximally Symmetric Solutions Of Einstein-Aether Theory

Einstein-aether theory is a generally covariant model in which local Lorentz invariance is broken by a dynamical unit timelike vector field!–aether.This model makes it viable to study gravitational and cosmic outcomes of preferred frame effects such as high-frequency dispersion or"variable speed of light",while retaining the generally covariant theory of gravitational metric.This dissertation limits attention to the effective theory of aether,which deals only with the antisymmetric derivative?_[#u_$].Then the aether has two massless transverse excitations,and the model’s solutions include all vacuum solutions of general relativity.There is evidence that Newton and Einstein’s theory of gravity cannot explain the dynamics of the universe,which consists entirely of baryons and radiation.To be able to understand the nature of galaxies,galaxy clusters,and the whole universe,invoking the existence of dark matter has become commonplace.Another approach is to modify the gravitational field equations to accommodate observations.Working in isotropic coordinates,we get some maximally symmetric nonrotating solutions of the Einstein-aether theory in 2+1 dimensions.Curvature singularities are not found in the Ricci and Kretschmann scalars,while conical singularities are avoidable by fixing some integration constants.