Singularity and Lorentzianity

Title: Singularity and Lorentzianity

Author: Ding Jia

Abstract: Spacetime singularities can arise as obstacles to maintaining the Lorentzian signature of the metric. Such Lorentzian singularities can be characterized as curvature singularities lacking continuous or less regular metric extensions. Lorentzian singularities may be overcome with a Lorentzian-constrained gravitational action principle. The piecewise Lorentzian solutions provide a dynamical extension of C⁰-inextendible spacetimes beyond the singularity.

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• Article v1.0: original version