Warping of the space-time surfaces and dielectric constant

The flat warped space-time surfaces are characterized by the reduced light-velocity &beta; 0 =c # /c&le; 1. There is a criticality with respect to the variations of c # (instability of metal plates illustrates this). Also the twisted Hamilton-Jacobi structures would be characterized by c # (see this ). The criticality of the warping could induce or accompany various kinds of quantum criticalities.…