The discussion sections begin with the famous Bekenstein bound, as to be addressed to black-body radiation, eventually. The advantage is quickly forced Hawking radiation connecting with thermal conduction handling object of black holes. Of course, where Newton method is used to unfold the frustration of numerical method when undergoing approximately acquired the routine of Triple-Alpha Process. The black hole’s entropy is denoted as well-known:

$S_{BH}=\frac{k_{B}A}{4l_p^2}$ (1)

Via entropy derivations, we obtain that the parameter 4T represents in Equation (1). This origins from the thermal conductivity possesses 4-directions $a_{r_1},a_{r_2},a_{r_3},a_{r_4}$:

$S=\frac{\left|\Delta Q\right|}{T^{\prime }}=\frac{1}{4\Delta T}\left|{\displaystyle \underset{i=1}{\overset{4}{\sum }}{Q}_i\left(r_0\right)-Q_0\left(R\right)}\right|=\frac{E_{B.E.}}{4\left(T-T_0\right)}\propto \frac{1}{4}$ (2)

where $E_{B.E.}=M{c}^2$ and $T^{\prime }\stackrel{up}{=}4\Delta T$. Followings resulted in

$S_{BH}=\frac{M{c}^2}{4\Delta T}$ (3)

Apply $M=\frac{r{c}^2\hslash }{2G\hslash }$ substituted into Equation (3). Therefore

$\begin{array}{l}{S}_{BH}=\frac{\stackrel{=A_{BH}}{\stackrel{︷}{4\pi r^2}}}{4\Delta T}\frac{\hslash c/\left(8\pi r\right)}{G\hslash /c^3}=\frac{4\pi r^2}{4}\frac{\stackrel{=\left[k_B\right]}{\stackrel{︷}{\hslash c/\left(8\pi r\Delta T\right)}}}{{\sqrt{G\hslash /c^3}}^2},\\ S_{BH}=\frac{k_{B}A}{4l_p^2}\end{array}$ (4)

This reproduction is very important since it helps one to think the physical sense of form of black hole that required main sequence stars ( $\ge 25M_{\Theta }$) raised-up the temperature $T\to 4T$ in the evolution process of collapse.

The material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy. As a result, it cannot support itself by the heat generated by fusion against gravity-collapse, but is supported only by electron degeneracy pressure, causing it to be extremely dense. The physics of degeneracy yields a maximum mass for a non-rotating white dwarf, the Chandrasekhar limit, approximately $1.44M_{�}$, beyond which it cannot be supported by electron degeneracy pressure.

White dwarf masses < $10M_{�}$ is located on in general case. The main mode of heat transfer belongs to thermal radiation, but to a certain extent, the problem of white dwarfs can be regarded as through conductive photometric transfer.

$\frac{\text{d}T}{\text{d}r}=-\frac{1}{k}{Q}_r=-\frac{1}{k}\frac{l}{4\pi r^2}$ (5)

Therefore

$\begin{array}{l}\frac{\text{d}T}{\text{d}r}=-\frac{1}{k}\frac{l}{4\pi r^2},\\ {\displaystyle \underset{T_0}{\overset{T}{\int }}4\text{d}T}=-\frac{l}{k\pi }{\displaystyle \underset{r=R}{\overset{r=r_0}{\int }}\frac{1}{r^2}\text{d}r}\end{array}$ (6)

Obviously, we get “four times original temperature expanded in radial directions”

$4\left(T-T_0\right)=\frac{l}{k\pi }\left(\frac{1}{r_0}-\frac{1}{R}\right)$ (7)

This equation contained magic number 4 such actually appeals one that black hole Hawking radiation could be derived the corresponding equation of black hole’s black body spectrum (i.e., Stephan-Boltzmann function) M. Hawking desired. As such, this equation is flavored and helpful. Of course above deduction is based on the conclusion that resulted in Bekenstein bound.

The majority mode of heat transfer on the neutron star $\left(1.5M_{\Theta }<M\le 3.2M_{\Theta }\right)$ surface belongs to the thermal convection. Indicated local heat flux is heat convention and is expressed as

$\stackrel{\dot{}}{Q}\equiv {\nabla }^2{Q}_r=h\left(T_s-T_{\infty }\right)=h\left(T-T_0\right),T>T_0$ (8)

Therefore

$h\left(T-T_0\right)=l\cdot {\nabla }^2\frac{1}{4\pi r^2}=\frac{-l}{2\pi r^3},r=r_0\to 0\left(\text{core}\right),r=R\left(\text{surface}\right)$ (9)

And [2] ²,

$\underset{T\to T_0}{\lim }\bar{h}\left(T-T_0\right)\stackrel{\left(L.H.\right)}{=}\frac{\stackrel{\dot{}}{Q}}{6\pi r^2}$ (10)

Followings,

$\begin{array}{l}\bar{h}\equiv \underset{T\to T_0}{\lim }\frac{\stackrel{\dot{}}{Q}}{4\cdot \left(3\pi r^2/2\right)\left(T-T_0\right)}=\frac{1}{4\left(T-T_0\right)}\underset{T\to T_0}{\lim }\frac{\stackrel{\dot{}}{Q}}{3\pi r^2/2},\\ \frac{2}{3}\left(T-T_0\right)\equiv \frac{\stackrel{\dot{}}{Q}}{\bar{h}\left(4\pi r^2\right)},0<r\le R\\ \frac{1}{3}\left(T-T_0\right)\equiv \frac{\stackrel{\dot{}}{Q}}{h\left(4\pi r^2\right)},0<r\le R\end{array}$ (11)

Due to $4\pi \approx 0.5+4\cdot 3!/2$, $4\pi h=h\left(0.5+4\cdot 3!/2\right)=1/3$, thus we have Heat Transfer Coefficients $h=\frac{1}{3\left(0.5+4\cdot 3!/2\right)}\approx 0.027$ [W/m²K]¹. By this thread, see Triple-Alpha Process. And due to Equation (10), such both lead that the surface R to the inner-core $r_0$ of neutron stars the heat convention corresponds to SUPERFLOW coefficients (i.e., SUPERFLUIDITY). Supposed that its physical behaviors are like ⁴He (I/II) [or superglass/supersolid] in regions of strong magnetic fields, otherwise ³He in the outer core through 9 km of neutron stars (i.e., regions of weak magnetic fields) [1] [2] . This mathematical deduction by factorial ( $n!$) for cosmology-physics is well to use, because it can reduce the complexities of deduction process.

Based on the previous deductions and the logics, we can think that the one of the three mode heat transfers such can be worked out the famous black hole’s perfect black body radiation formula that Hawking desired. Here the thermal conduction is the definite option as deduction and does not violate any fundamental physical principle. In detailed:

$4\left(T-T_0\right)=\frac{l}{k\pi }\left(\frac{1}{r_0}-\frac{1}{R}\right),r_0\to 0\left(\text{singularity}\right),R=r_s$ (12.1)

$4\left(T-T_0\right)=\underset{\begin{array}{c}{r}_0\to 0\\ M\to \infty \end{array}}{\lim }\frac{l}{k\pi }\left(\frac{1}{r_0}-\frac{c^2}{2GM}\right),$ (12.2)

$4\cdot \pi \cdot k\left(T-T_0\right)=\underset{\begin{array}{c}{r}_0\to 0\\ M\to \infty \end{array}}{\lim }l\left(\frac{1}{r_0}-\frac{c^2}{2GM}\right),$ (12.3)

$\begin{array}{l}4!{\displaystyle \underset{T_0}{\overset{T}{\int }}{\displaystyle \underset{T_0}{\overset{T}{\int }}{\displaystyle \underset{T_0}{\overset{T}{\int }}{\displaystyle \underset{T_0}{\overset{T}{\int }}\left(T-T_0\right){\text{d}}^{4}T}}}}={\displaystyle \underset{M}{\int }{\displaystyle \underset{M}{\int }{\displaystyle \underset{M}{\int }{\displaystyle \underset{M}{\int }\underset{\begin{array}{c}{r}_0\to 0\\ M\to \infty \end{array}}{\lim }l\left(\frac{1}{r_0}-\frac{c^2}{2GM}\right){\text{d}}^{4}M}}}},\\ K\left(T^4-T_0^4\right)={\displaystyle \underset{M}{\int }{\displaystyle \underset{M}{\int }{\displaystyle \underset{M}{\int }{\displaystyle \underset{M}{\int }\underset{\begin{array}{c}{r}_0\to 0\\ M\to \infty \end{array}}{\lim }l\left(\frac{1}{r_0}-\frac{c^2}{2GM}\right){\text{d}}^{4}M}}}},K=const=A_{BH}\epsilon \sigma \\ A_{BH}\sigma \epsilon \left(T^4-T_0^4\right)={\displaystyle \underset{M}{\int }{\displaystyle \underset{M}{\int }{\displaystyle \underset{M}{\int }{\displaystyle \underset{M}{\int }\underset{\begin{array}{c}{r}_0\to 0\\ M\to \infty \end{array}}{\lim }l\left(\frac{1}{r_0}-\frac{c^2}{2GM}\right){\text{d}}^{4}M}}}}\end{array}\}$ (12.4)

For black holes $l=0$ and via observation, the terms inside this bracket resulted in $\infty -\infty$. As such, we obtained ${\displaystyle \underset{M}{\int }\underset{\begin{array}{c}{r}_0\to 0\\ M\to \infty \end{array}}{\lim }l\left(\frac{1}{r_0}-\frac{c^2}{2GM}\right)\text{d}M}=finite$ (e.g. power of back-body radiation). So far, the famous black hole’s perfect black body radiation formula Hawking desired is now derived:

$P_{BH}=A_{BH}\sigma \epsilon \left(T^4-T_0^4\right)$ (13)

Based on the above calculation, via investigation of tables of material thermal conductivities, we found that k = 1.909 W·m⁻¹·K⁻¹ (thermal conductivity) corresponds to material made of china/porcelains. As a result, we can think that black holes if were in touch, would be felt like ordinary porcelains, and only if gravity were not taken into consideration (actually this is impossible). As such, it would be such interesting. This thermal property is exactly corresponding to Ads/CFT correspondence since as a material of porcelains, it saves information or lets information escape is not strange.