Neutron stars and colour force

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Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
selfAdjoint
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As I unserstand it, the quarks would become unconfined and constitute a gas. The thermodynamics of this gas is under study by theoreticians.

Gluons carry two color charges, or rather a color and an anticolor; they will be attractive if the color algebra can be satisfied. But if a quark has the same color, or anticolor as a gluon then they will repel. Like charges still repel. Note the important fact that gluons can attract/repel each other too.
 
  • #3
Chronos
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Try a search using 'quark star'. You may find that interesting.
 
  • #4
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Pretential Pressure...


A repulsive force could stop the collapse of the neutron star in place of neutron degeneracy pressure.



Classical Gravitational Pressure: (negative)
[tex]P_g = \frac{G M_s^2}{4 \pi r_s^4}[/tex]

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

[tex]r_o = 1.5*10^{-15} m[/tex] - nuclear radius
[tex]r_1[/tex] - internuclear radius
[tex]r_s[/tex] - stellar radius
[tex]f[/tex] - nuclear interaction strength (positive)

Orion1 Criterion:
[tex]P_g = P_y[/tex]

[tex]\frac{G M_s^2}{4 \pi r_s^4} = f^2 \frac{e^{- \frac{r_1}{r_0}}}{4 \pi r_s^2 r_1^2}[/tex]

Orion1-Yukawa Critical Mass:
[tex]M_c = f \frac{r_s}{r_1} \sqrt{ \frac{e^{- \frac{r_1}{r_0}}}{G}}[/tex]
[tex]r_1 < r_0[/tex]

Based upon the Orion1 solution, what is the critical mass magnitude of a Kurious Neutron Star?

 
  • #5
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One should be very careful here. Under the high density assumption, the formula for classical graviational pressure may have to be replaced by the GR equivalent. (For a neutron star, I am told that this is a correction of about 10%; it would be higher for more dense objects). One thing is certain: in classical GR, once matter collapses inside its Schwarzschild radius, (or some other radius for more complex - eg rotational - spacetime geometries) no force can prevent the collapse to a singularity no matter how powerful. This is because the world lines of particles must lie within the light cones, and the light cones point towards the singularity.
 
  • #6
Could the repulsive gravitational effect of dark energy stop the particles from lying within the light cones?
 
  • #7
970
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Chandresekhar Criterion...

Under the high density assumption, the formula for classical graviational pressure may have to be replaced by the GR equivalent. (For a neutron star, I am told that this is a correction of about 10%; it would be higher for more dense objects). One thing is certain: in classical GR, once matter collapses inside its Schwarzschild radius,...

Orion1-Yukawa Critical Mass:
[tex]M_c = f \frac{r_s}{r_1} \sqrt{ \frac{e^{- \frac{r_1}{r_0}}}{G}}[/tex]

[tex]r_1 < r_0[/tex]

Classical GR Chandresekhar Radius:
[tex]r_{c} = \frac{2GM_c}{c^2}[/tex]

Chandresekhar Criterion:
[tex]r_s <= r_{c}[/tex]

[tex]r_s <= \frac{2GM_c}{c^2}[/tex]

[tex]M_{ch} = \frac{r_c c^2}{2G}[/tex]

Classical Chandresekhar-Yukawa Mass Limit:
[tex]M_c = M_{ch}[/tex]

[tex]\frac{r_c c^2}{2G} = f \frac{r_s}{r_1} \sqrt{ \frac{e^{- \frac{r_1}{r_0}}}{G}}[/tex]

[tex]r_s = r_c[/tex]

[tex]\frac{c^2}{2G} = \frac{f}{r_1} \sqrt{ \frac{e^{- \frac{r_1}{r_0}}}{G}}[/tex]

Chandresekhar-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 solution, what is the magnitude of the Chandresekhar-Yukawa Limit?

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

 
Last edited:
  • #8
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Relative Relation...

Under the high density assumption, the formula for classical graviational pressure may have to be replaced by the GR equivalent. (For a neutron star, I am told that this is a correction of about 10%; it would be higher for more dense objects).

What is the exact GR formula for gravitational pressure?
 
  • #9
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Rothiemurchus said:
Could the repulsive gravitational effect of dark energy stop the particles from lying within the light cones?
Not unless it can exert an infinite force :smile:
orion1 said:
What is the exact GR formula for gravitational pressure?
I wish I knew... try the GR forum?
What I can tell you is that when one studies motion in a Scharzschild metric, the post-Newtonian effects are encoded in an additional attractive 1/r^3 term in the potential. Still, I don't think it would be correct to take the derivative of that and throw in an additional 1/r^4 attractive force. It's not conceptually correct in any event (there is no gravitational force or local field energy in GR), and I don't know if it would give a correct answer. I strongly suggest asking one of the local GR experts.
 
  • #10
970
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Gravity Gyruss...


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]

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]

Reference:
http://super.colorado.edu/~michaele/Lambda/gr.html [Broken]

 
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  • #11
970
3
Lame Latex...

Latex Generator Failure.


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]

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]

Reference:
http://super.colorado.edu/~michaele/Lambda/gr.html [Broken]


Could someone please repost my Latex source code? My Latex Generator has failed. (just remove '!' symbol from [!tex])
 
Last edited by a moderator:

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