# Einstein Probabilistic Units/Black Holes

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### Black Hole

A black hole can be defined by the Schwarzschild radius

${\displaystyle r_{s}={\frac {2GM_{bh}}{c^{2}}}}$

Expressing this using Einstein Probabilistic Units

${\displaystyle r_{bh}={2BM_{bh}}}$

Solving for B give us

${\displaystyle B_{bh}={\frac {r_{bh}}{2M_{bh}}}}$

The following table shows some properties of Black Hole using Einstein's Probabilistic Units (EPU);

 Property Equation EPU Mass ${\displaystyle M_{s}=2\;{\frac {1}{r_{s}}}{\frac {G}{c^{2}}}}$ ${\displaystyle M_{s}={\frac {2\;c}{A_{s}\;B_{s}}}}$ ${\displaystyle M_{s}={\frac {c}{B_{0}}}\;{\frac {A_{s}}{A_{0}^{2}}}}$ Schwarzschild radius ${\displaystyle r_{s}=2\;M_{s}{\frac {G}{c^{2}}}}$ ${\displaystyle r_{s}=2\;M_{s}\;B_{0}}$ ${\displaystyle B_{0}={\frac {G}{c^{2}}}={\frac {1}{2}}\;B_{s}}$ Area ${\displaystyle A_{s}=16\;\pi \;M_{s}^{2}{\frac {G^{2}}{c^{4}}}}$ ${\displaystyle A_{s}=16\pi \;M_{s}^{2}\;B_{0}^{2}}$ ${\displaystyle B_{0}^{2}={\frac {1}{16\;\pi }}\;B_{s}^{2}}$ Density ${\displaystyle \rho _{s}={\frac {3}{32\pi }}{\frac {c^{6}}{M_{s}^{2}\;G^{3}}}}$ ${\displaystyle \rho _{s}={\frac {3}{32\pi }}{\frac {1}{M_{s}^{2}}}{\frac {1}{B_{0}^{3}}}}$ ${\displaystyle \rho _{s}={\frac {3}{8\pi }}{\frac {1}{B_{0}}}{\frac {1}{r_{s}^{2}}}}$ Entropy ${\displaystyle S_{BH}={\frac {1}{4}}\;k_{B}{\frac {A_{s}}{l_{P}^{2}}}}$ ${\displaystyle S_{BH}={\frac {1}{4}}\;k_{B}{\frac {B_{s}}{B_{0}}}}$ ${\displaystyle B_{0}={\frac {1}{4}}\;k_{B}{\frac {B_{s}}{S_{BH}}}}$ Temperature ${\displaystyle T={\frac {1}{8\;\pi }}{\frac {1}{M_{s}}}{\frac {\hbar \;c}{k_{B}}}{\frac {c^{2}}{G}}}$ ${\displaystyle }$ ${\displaystyle }$

### Entropy

The Bekenstein–Hawking formula for black-hole entropy is proportional to the area of its event horizon A.

${\displaystyle S_{BH}={\frac {k_{B}A_{s}}{4\;l_{P}^{2}}}={\frac {k_{B}\;c^{3}\;A_{s}}{4\;G\;\hbar }}\;{\frac {J}{K}}}$

Using Einstein's Probabilistic units to express Bekenstein–Hawking formula;

${\displaystyle S_{BH}=k_{B}\;{\frac {c^{3}}{\hbar }}\;{\frac {A_{s}}{c^{2}}}\;{\frac {c^{2}}{G}}=k_{B}\;{\frac {c^{3}}{\hbar }}\;{\frac {1}{\upsilon _{s}^{2}}}\;{\frac {1}{B_{0}}}=k_{B}\;{\frac {B_{s}}{B_{0}}}=Constant\;{\frac {1}{\upsilon _{s}^{2}}}=-k_{B}\;}$

${\displaystyle S_{BH}=k_{B}\;ln(W)=k_{B}\;{\frac {B_{s}}{B_{0}}}=k_{B}\;{\frac {A_{0}^{2}}{A_{S}^{2}}}}$

${\displaystyle W=e^{S/k_{B}}=e^{B_{s}/B_{0}}}$

${\displaystyle T_{H}={\dfrac {\hbar c^{3}}{8\pi \;GMk_{B}}}}$
${\displaystyle T_{H}={\dfrac {\hbar c^{3}}{8\pi \;\mu _{M}k_{B}}}={\frac {\hbar c}{8\pi k_{B}}}\times {\frac {m^{2}}{s^{2}}}{\frac {s^{2}}{m^{3}}}={\frac {1}{8\pi k_{B}}}{\frac {Q^{2}}{m}}}$
${\displaystyle T_{H}={\dfrac {1}{8\pi }}{\dfrac {\hbar c}{M}}{\dfrac {1}{B_{0}}}{\dfrac {1}{k_{B}}}={\dfrac {1}{8\pi }}{\dfrac {\mu }{B_{0}}}{\dfrac {1}{k_{B}}}}$
${\displaystyle B_{0}={\dfrac {1}{8\pi }}{\dfrac {\mu _{M}}{T_{H}}}{\dfrac {1}{k_{B}}}}$
${\displaystyle B={\dfrac {hc}{\left(T_{H}k_{B}\right)M_{\odot }}}}$
${\displaystyle T_{\mathrm {H} }={\frac {\hbar c^{3}}{8\pi GMk_{\mathrm {B} }}}}$