Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Can the "brick wall" model present the same results in different
  coordinate representations?   By using the 't Hooft's "brick wall" model and the Pauli-Villars
regularization scheme we calculate the statistical-mechanical entropies arising
from the quantum scalar field in different coordinate settings, such as the
Painlev\'{e} and Lemaitre coordinates. At first glance, it seems that the
entropies would be different from that in the standard Schwarzschild coordinate
since the metrics in both the Painlev\'{e} and Lemaitre coordinates do not
possess the singularity at the event horizon as that in the Schwarzschild-like
coordinate. However, after an exact calculation we find that, up to the
subleading correction, the statistical-mechanical entropies in these
coordinates are equivalent to that in the Schwarzschild-like coordinate. The
result is not only valid for black holes and de Sitter spaces, but also for the
case that the quantum field exerts back reaction on the gravitational field
provided that the back reaction does not alter the symmetry of the spacetime.

15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas