Einstein spacetimes with weak regularity

TL;DR

This paper reviews recent developments in the study of Einstein spacetimes with weak regularity, focusing on the construction of spacetimes where impulsive gravitational waves and shock waves propagate under weak curvature conditions.

Contribution

It introduces the concept of weakly regular Einstein spacetimes and discusses their construction, expanding understanding of solutions with low regularity in general relativity.

Findings

Construction of weakly regular Einstein spacetimes

Propagation of impulsive gravitational waves

Propagation of shock waves in weak regularity settings

Abstract

We review recent work on the Einstein equations of general relativity when the curvature is defined in a weak sense. Weakly regular spacetimes are constructed, in which impulsive gravitational waves, as well as shock waves, propagate.