I have come across the statement that propagation of singularities is a general feature of the hyperbolic equations (context: Einstein Field Equations). Even on an intuitive level, I cannot make sense out of it. To me it seems, that then any initial data we take will already contain the (Big Bang-) singularity, and therefore there is no such thing as a regular initial data.
Since Einstein Equations are hyperbolic, it means then that they will always (?!?) propagate the initial singularity? I would be grateful if anyone could explain how, in the context of general relativity, to understand the statement about the singularity propagation correctly. Thanks!