Einstein Probabilistic Units/Black Holes

This resource includes primary and/or secondary research.

Black Hole
A black hole can be defined by the Schwarzschild radius


 * $$ r_s = \frac{2 G M_{bh}}{c^2} $$

Expressing this using Einstein Probabilistic Units


 * $$ r_{bh} = {2 B M_{bh}} $$

Solving for B give us


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

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

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

$$S_{BH}=\frac{k_BA_s}{4\;l^2_P}= \frac{k_B\;c^3\;A_s}{4\;G\;\hbar}\;\frac{J}{K}$$

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

$$S_{BH}=k_B\;\frac{c^3}{\hbar}\;\frac{A_s}{c^2}\;\frac{c^2}{G}=k_B\;\frac{c^3}{\hbar}\;\frac{1}{\upsilon^2_s}\;\frac{1}{B_0} =k_B\;\frac{B_s}{B_0}=Constant\;\frac{1}{\upsilon^2 _s}=-k_B\; $$

$$S_{BH}=k_B\;ln(W)=k_B\;\frac{B_s}{B_0}=k_B\;\frac{A_0^2}{A_S^2}$$

$$W=e^{S/k_B}=e^{B_s/B_0}$$

Hawking radiation temperature
$$T_{H}=\dfrac{\hbar c^{3}}{8\pi\;GMk_{B}}$$

$$T_{H}=\dfrac{\hbar c^{3}}{8\pi\;\mu_M k_{B}}=\frac{\hbar c}{8\pi k_B}\times \frac{m^2}{s^2}\frac{s^2}{m^3}=\frac{1}{8\pi k_B}\frac{Q^2}{m} $$

$$T_{H}=\dfrac{1}{8\pi }\dfrac{\hbar c}{M}\dfrac{1}{B_{0}}\dfrac{1}{k_{B}}=\dfrac{1}{8\pi }\dfrac{\mu }{B_{0}}\dfrac{1}{k_{B}}$$

$$B_{0}=\dfrac{1}{8\pi }\dfrac{\mu_M }{T_{H}}\dfrac{1}{k_{B}}$$

$$B=\dfrac{hc}{\left( T_{H}k_{B}\right) M_{\odot}}$$

$$T_\mathrm{H} = \frac{\hbar c^3}{8 \pi G M k_\mathrm{B}}$$