Statistical-Mechanical Entropies of Schwarzschild Black Holedue to Arbitrary Spin Fields in Different Coordinates

Abstract

The statistical-mechanical entropies of the Schwarzschild black holearising from the scalar, Weyl neutrino, electromagnetic,Rarita–Schwinger and gravitational fields are investigated in thePainlevé and Lemaitre coordinates. Although the metrics in thePainlevé and the Lemaitre coordinates do not obviously possess thesingularity as that in the Schwarzschild coordinate, we find that theentropies of the arbitrary spin fields in both the Painlevé andLemaitre coordinates are exactly equivalent to that in the Schwarzschildcoordinate.