Rotating black hole entropy from two different viewpoints

Using the brick-wall method, we study the entropy of Kerr-Newman black hole from two different viewpoints, a rest observer at infinity and a zero angular momentum observer near the horizon. We investigate this with a scalar field in the canonical quantization approach. An observer at infinity can take one of the two possible frequency ranges; one is with positive frequencies only and the other is with the whole range including negative frequencies. On the other hand, a zero angular momentum observer near horizon can take positive frequencies only. For the observer at infinity, the superradiant modes appear in either choice of the frequency ranges and the two results coincide. For the zero angular momentum observer superradiant modes do not appear due to the absence of the ergoregion. The resulting entropies from the two viewpoints turn out to be the same.