Given any time function on a spacetime M, we define an induced *null-distance* function, built from and closely related to the causal
structure of M. This null-distance is a conformal pseudometric in
general, but is positive-definite under natural conditions. Further, in
basic model cases, the causal structure is encoded completely in the
resulting metric space.

In the cosmological setting, a canonical choice
of time function was introduced and studied by Andersson, Galloway, and
Howard. We show that under their basic `niceness' condition, the induced
null distance is definite, and hence provides a uniform way of encoding
`big bang' and related spacetimes as metric spaces. This is joint work
with Christina Sormani.