The Ergo Region of the Kerr Black Hole in the Isotropic Coordinate

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The isotropic coordinate is the more physically meaningful coordinate in the Schwarzschild black hole. Then we apply this isotropic coordinate to the Kerr black hole, and we have found the ergo region does not appear and all metrices gμν become regular even at the “event horizon” in this coordinate. But the determinant det gμν becomes zero at the “event horizon”, which means that gμν becomes singular at the “event horizon”.