IS THE LORENTZ SYMMETRY EXACT?

A theory that allows for the break of the Lorentz symmetry in the tangent space-time within a Riemannian geometric framework was studied. The conclusion is that the Riemannian geometry is not compatible with the absence of an exact Lorentz symmetry in the tangent space-time. If one wants to explore the consequences of Lorentz symmetry breaking in four dimensions other ways must be tried and/or a higher number of dimensions must be considered.