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By using the Newman-Penrose formalism and the improved thin-layer ``brickwall'' approach, the statistical-mechanical entropies of the Schwarzschild-deSitter black hole arising from quantum massless arbitrary spin fields arestudied in the Painlev\'e and Lemaitre coordinates. Although the metrics inboth the Painlev\'e and the Lemaitre coordinates do not obviously possess thesingularities as that in the Schwarzschild-like coordinate, we find that, forarbitrary spin fields, the entropies in the Painlev\'e and Lemaitre coordinatesare exactly equivalent to that in the Schwarzschild-like coordinate.

Entropy of the Schwarzschild-de Sitter Black Hole due to arbitrary spin fields in different Coordinates