Let’s see if we just choose the first part in \eqref{eq:bw-s}, how the entropy looks like, and it’s meanings. Schwarzschild black hole’s surface gravity is
\begin{equation}
\kappa = \frac{1}{4M}, \\
\end{equation}
and $\beta = \frac{1}{T_H}=\frac{2\pi}{\kappa}=8\pi M $, $r_H = 2M $ is the event horizon, then the entropy is
\begin{equation}
S=\frac{2M}{360h}.
\end{equation}
If we choose the cutoff as
\begin{equation}\label{eq:bw-cutoff}
h=\frac{T_H}{90}=\frac{1}{720\pi M}=\frac{1}{90\beta},
\end{equation}
then the entropy becomes
\begin{equation}
S=4\pi M^2=\pi r_H^2=\frac{1}{4}A.
\end{equation}
where \(A=4\pi r_H^2\) is the area of the event horizon. The entropy is the Bekenstein-Hawking entropy.

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