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Neutron stars and colour force

  1. Sep 17, 2004 #1


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

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

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

    Einstein-Yukawa criterion:
    [tex]P_e = P_y[/tex]

    [tex]\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}[/tex]

    Is this criterion conceptually correct?

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

    Based upon the Orion1 equasions, what are the Standard International (SI) units for [tex]f_1[/tex] ?

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

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

    Classical Einstein-Schwarzschild critical density:
    [tex]\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)[/tex]

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

    Based upon the Orion1 equasions, what are the Standard International (SI) units for [tex]\nabla[/tex] and [tex]\phi[/tex]?

    Reference:
    http://super.colorado.edu/~michaele/Lambda/gr.html
    https://www.physicsforums.com/showthread.php?t=40562
     
    Last edited: Sep 18, 2004
  2. jcsd
  3. Sep 22, 2004 #2
    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.
     
  4. Sep 25, 2004 #3
    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 [tex]\nabla[/tex]?
     
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