[math-fun] Kerr metric

As far as I know, an important still-open problem is to find a way to glue the Kerr vacuum metric as the exterior, onto the metric of some realistic hunk of rotating matter as the interior, to get combined metric representing a rotating mass and its gravity field. Seems quite embarrassing that nobody has been able to do that. How hard can it be? (But there are many successful ways to do this in the non-rotating case.)