When the event horizon is rotating at the speed of light in a 'maximal Kerr' black hole. The geometry of such holes is different from a non-rotating 'Schwarschild' black hole because the event horizon and the surface of infinite redshift do not coincide and you end up along the equatorial plane, with two 'horizon like' surfaces. Only the inner event horizon is 'fatal'. The zone between the outer surface and the inner horizon, called the 'ergosphere' is traversable and has some interesting physical aspects to it where you can extract energy from the black hole. The above image is a ray trace of what the emission from an accretion disk of gas would look like around a Kerr black hole viewed at an inclination of 30 degrees from face-on. (figure courtesy of C. Perez, Stanford University)

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