Reduced Circumference: Schwarzschild vs Kerr Metric

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The r-coordinate in the Schwarzschild metric represents the reduced circumference, but in the Kerr metric, it does not serve the same purpose. The discussion highlights the confusion surrounding the interpretation of the r-coordinate in the Kerr metric. A suggestion is made that a coordinate change could lead to a form where R(r) represents the reduced circumference for the azimuthal angle φ. This implies that while r in the Kerr metric is not the reduced circumference, it may have a different physical significance. Understanding these differences is crucial for grasping the implications of the Kerr solution in general relativity.
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Okay, I understand that the r-coordinate in the Schwarzschild metric represents the reduce circumference. My problem is that the r-coordinate in the Kerr metric is NOT the reduced circumference! What is it? Somebody, please answer this as quickly and as painlessly as possible!
Thank You
 
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Right, it is not. What is it? Sorry, I don’t know... I guess that if you make a coordinate change in a way that you get \inline{R(r)^2 d{\phi}^2} then \inline{R} will be the reduced circumference for \inline{\phi}}. May be this can give you a hint about a possible physical meaning of \inline{r}.
 

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