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

The statistical-mechanical entropies of the Schwarzschild black hole arising from the scalar, Weyl neutrino, electromagnetic, Rarita--Schwinger and gravitational fields are investigated in the Painleve and Lemaitre coordinates. Although the metrics in the Painleve and the Lemaitre coordinates do not obviously possess the singularity as that in the Schwarzschild coordinate, we find that the entropies of the arbitrary spin fields in both the Painleve and
Lemaitre coordinates are exactly equivalent to that in the Schwarzschild
coordinate.