Stability of infinitesimal linearity

Determine whether linearity at the infinitesimal level is stable under the convergence theories for metric spacetimes.

Background

The paper describes compactness and stability for Lorentzian metric-spacetime convergence as being at an early stage. In this context, the authors identify stability of linearity at the infinitesimal level as an unresolved problem. This property is related to distinguishing Lorentzian-like spacetimes from more general Finsler-like structures and is analogous to infinitesimal Hilbertianity in positive-signature metric measure geometry.