On the differentiability of Cauchy horizons

TL;DR

This paper proves that in certain classes of spacetimes, Cauchy horizons are generically densely nondifferentiable, extending previous constructions and implications for black hole event horizons.

Contribution

It establishes the genericity of densely nondifferentiable Cauchy horizons within a specific class, linking to partial Cauchy surfaces and black hole horizons.

Findings

Densely nondifferentiable Cauchy horizons are generic in certain classes.

Existence of such horizons from partial Cauchy surfaces.

Implications for black hole event horizon differentiability.

Abstract

Chrusciel and Galloway constructed a Cauchy horizon that is nondifferentiable on a dense set. We prove that in a certain class of Cauchy horizons densely nondifferentiable Cauchy horizons are generic. We show that our class of densely nondifferentiable Cauchy horizons implies the existence of densely nondifferentiable Cauchy horizons arising from partial Cauchy surfaces and also the existence of densely nondifferentiable black hole event horizons.