Regularity of curve integrable spacetimes

Abstract

The idea of defining a gravitational singularity as an obstruction to the dynamical evolution of a test field (described by a PDE) rather than the dynamical evolution of a particle (described by a geodesics) is explored. In particular, the concept of field regularity is introduced which serves to describe the well-posedness of the local initial value problem for a given field.In particular this is applied to (classical) scalar fields in the class of curve integrable spacetimes to show that the classical singularities do not interrupt the well-posedness of the wave equation.

arXiv comment28 pages, 1 figure

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• Spacetime singularities and curvature blow-ups
• Generalised hyperbolicity in spacetimes with Lipschitz regularity
• Generalised hyperbolicity in spacetimes with string-like singularities