What is a shell-crossing singularity?

Abstract

AbstractA 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 C2 singularity which is C1 regular, that is it can be transformed away by a C1 coordinate transformation.