# Neutron stars and colour force

1. Sep 17, 2004

### Orion1

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 equasions, 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 equasions, what are the Standard International (SI) units for $$\nabla$$ and $$\phi$$?

Reference:

Last edited: Sep 18, 2004
2. Sep 22, 2004

### 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.

3. Sep 25, 2004

### Orion1

Nabla Nexus...

SI = Système International (International System)

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

Is this correct? Can anyone present a mathematical demonstration example of this dimentionless operator $$\nabla$$?