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By using the 't Hooft's "brick wall" model and the Pauli-Villarsregularization scheme we calculate the statistical-mechanical entropies arisingfrom the quantum scalar field in different coordinate settings, such as thePainlev\'{e} and Lemaitre coordinates. At first glance, it seems that theentropies would be different from that in the standard Schwarzschild coordinatesince the metrics in both the Painlev\'{e} and Lemaitre coordinates do notpossess the singularity at the event horizon as that in the Schwarzschild-likecoordinate. However, after an exact calculation we find that, up to thesubleading correction, the statistical-mechanical entropies in thesecoordinates are equivalent to that in the Schwarzschild-like coordinate. Theresult is not only valid for black holes and de Sitter spaces, but also for thecase that the quantum field exerts back reaction on the gravitational fieldprovided that the back reaction does not alter the symmetry of the spacetime.Comment: 8 pages, Phys. Rev. D in pres

Can the “brick wall” model present the same results in different coordinate representations?