Generic metrics satisfy the generic condition

TL;DR

This paper proves that the 'generic condition' in singularity theorems of general relativity is satisfied for a residual set of Lorentzian metrics, establishing its genericity in the space of such metrics.

Contribution

It demonstrates that the generic condition is satisfied for a residual set of Lorentzian metrics in the Whitney $C^k$-topology, providing a rigorous mathematical foundation.

Findings

The generic condition holds for all metrics in a residual set.

The proof applies to Lorentzian metrics on a given manifold.

The result depends on the dimension of the manifold.

Abstract

We prove that the "generic condition" used in singularity theorems of general relativity is generic in the space of Lorentzian metrics on a given manifold, in the sense that it is satisfied for all metrics in a residual set in the Whitney $C^k$-topology, for $k$ depending on the dimension of the manifold.