𝐻¹ solutions on curve integrable spacetimes

Abstract

In this work we use a framework based on scalar linear hyperbolic equations that characterises gravitational singularities as the obstruction to well-posedness. In particular, we show existence of H 1 H^{1} solutions on a certain class of curve integrable spacetimes. This implies that these spacetimes are not singular in the sense of obstructions to well-posedness even if their regularity is below C 2 C^{2} .