What is a shell-crossing singularity?

Abstract

Abstract A detailed discussion of Newtonian and general relativistic spherically symmetric dust solutions leads to the following suggested criteria for a singularity to be classified as a shell-cross : (1) All Jacobi fields have finite limits (in an orthonormal parallel propagated frame) as they approach the singularity. (2) The boundary region forms an essential C 2 singularity which is C 1 regular, that is it can be transformed away by a C 1 coordinate transformation.