http://mnras.oxfordjournals.org/content/162/4/307.abstract discusses observables of such metrics, especially Gödel's.
A 2009 overview (postdating COBE, for example): http://iopscience.iop.org/article/10.1088/0004-637X/703/1/35... (preprint: https://arxiv.org/abs/0902.4575)
> 2/3 LIGO detections imply one of the merging pair of black holes should be a naked singularity.
Where did you get that from?
It's sure not prominent on the caltech or mit sites, or indeed in Pretorius et al. https://arxiv.org/abs/1603.08955