What Is Geodesic Incompleteness in General Relativity?

[latentcorpse]

Singularities in GR are often associated with geodesic incompleteness.

My question is what does it actually mean for a geodesic to be incomplete?

 

[jdwood983]

From my vague understanding, geodesic incompleteness is when we can't extrapolate the function over all of space & time.

 

[latentcorpse]

yes but what about the t=0 big bang singularity. is this a singularity because we can only extrapolate geodesics as far back as to a time just after t=0 but we can't extend them to the t=0 region of spacetime itself and so the geodesics are incomplete?

 

[jdwood983]

yes but what about the t=0 big bang singularity. is this a singularity because we can only extrapolate geodesics as far back as to a time just after t=0 but we can't extend them to the t=0 region of spacetime itself and so the geodesics are incomplete?

From what I understand of GR, yes.