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A few questions related to frame dragging

I am trying to get my head around a few concepts related to frame dragging and related physics. In regards to black holes that have no charge and all thier mass is tied up in rotational kinetic ...
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Derivation of superluminality in astronomy

Can somebody provide derivation of the relativistic explanation of (apparent) superluminality in astronomy? The derivation on wikipedia seems to be a bit confusing.