Effect of Spin on Thermodynamical Quantities around Reissner--Nordström Black Holes

Using the quantization procedure involving in the Boulware vacuum state and Killing time t, we evaluate the entropy density, energy density, pressure and equation of state around the Reissner--Nordström black hole by the Wentzel--Kramers--Brillouin approximation on the Teukolsky-type master equation. We find that, near the event horizon, there exist subleading order terms with spin dependence beyond the expected Minkowskian high-temperature contribution. In particular, the terms are important and cannot be neglected for near-extremal black hole cases. At large r, the Boulware state approaches the Minkowski vacuum and the theory agrees with that performed in Minkowski spacetime.