Time kink: modeling change of metric signature

Abstract

The model of a signature change of a metric from the Lorenztian to Euclidean one with the use of a time dependent kink as $g_{00}$ component of the metric is considered. The metric which describes the continuous change of the signature of this type on a hypersurface is constructed and corresponding Einstein equations are solved in both regions of the space-time. The discontinuities of the Einstein tensor components on the hypersurface are discussed as well as junction conditions for the parameters of the solutions. Additionally, the properties of simple cosmological model are discussed in the model, the presence of an inflation in the model is demonstrated as a consequence of the signature change without any additional fields need. The possible appearance of this type of solution for the metric in the form of the scalar field in the framework of the Einstein-Cartan gravity is described. The Lagrangian for that field and it's properties are obtained as well as a time dependent potential of the field which separate the Lorentzian and Euclidean regions of the space-time