How Do Gluons Affect Neutron Star Stability?

[Orion1]

If neutrons stay intact and get closer together than 10^-15 metres in a neutron star, would the exchange of mesons between neutrons stop and be replaced by the exchange of gluons, and would the gluons cause an attractive or repulsive force between neutrons? A repulsive force could
stop the collapse of the neutron star in place of neutron degeneracy pressure.

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Einstein field equation gravitational potential:
$$\nabla^2 \phi = 4 \pi G \left( \rho + \frac{3P}{c^2} \right)$$

General Relativity gravitational pressure:
$$P_e = \frac{c^2}{3} \left( \frac{\nabla^2 \phi}{4 \pi G} - \rho \right)$$

Classical Yukawa Pressure:
$$P_y = f^2 \frac{e^{- \frac{r_1}{r_0}}}{4 \pi r_s^2 r_1^2}$$

Einstein-Yukawa criterion:
$$P_e = P_y$$

$$\frac{c^2}{3} \left( \frac{\nabla^2 \phi}{4 \pi G} - \rho \right) = f^2 \frac{e^{- \frac{r_1}{r_0}}}{4 \pi r_s^2 r_1^2}$$

Is this criterion conceptually correct?

Classical Schwarzschild-Yukawa nuclear interaction strength Limit:
$$f_1 = \frac{r_1c^2}{2} \sqrt{\frac{e^{\frac{r_1}{r_0}}}{G}}$$
$$r_1 < r_0$$

Based upon the Orion1 equations, what are the Standard International (SI) units for $$f_1$$ ?

$$\frac{c^2}{3} \left( \frac{\nabla^2 \phi}{4 \pi G} - \rho \right) = \frac{c^4}{16 \pi G r_s^2}$$

$$\left( \frac{\nabla^2 \phi}{4 \pi G} - \rho \right) = \frac{3 c^2}{16 \pi G r_s^2}$$

Classical Einstein-Schwarzschild critical density:
$$\rho_c = \left( \frac{\nabla^2 \phi}{4 \pi G} - \frac{3 c^2}{16 \pi G r_s^2} \right) = \frac{}{4 \pi G} \left( \nabla^2 \phi - \frac{3 c^2}{4 r_s^2} \right)$$

$$\rho_c = \frac{}{4 \pi G} \left( \nabla^2 \phi - \frac{3 c^2}{4 r_s^2} \right)$$

Based upon the Orion1 equations, what are the Standard International (SI) units for $$\nabla$$ and $$\phi$$?

Reference:
http://super.colorado.edu/~michaele/Lambda/gr.html
https://www.physicsforums.com/showthread.php?t=40562
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[Nylex]

I don't understand those equations, but I thought del/nabla was a differential operator and didn't have units. Also, SI = Système International, not Standard International.

 

[Orion1]

Nabla Nexus...


SI = Système International (International System)

I thought del/nabla was a differential operator and didn't have units.[/color]

Is this correct? Can anyone present a mathematical demonstration example of this dimensionless operator $$\nabla$$?[/color]