# Neutron stars and colour force

## 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.

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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.

Chronos
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Try a search using 'quark star'. You may find that interesting.

Pretential Pressure...

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

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

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

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

Orion1 Criterion:
$$P_g = P_y$$

$$\frac{G M_s^2}{4 \pi r_s^4} = f^2 \frac{e^{- \frac{r_1}{r_0}}}{4 \pi r_s^2 r_1^2}$$

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

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

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.

Could the repulsive gravitational effect of dark energy stop the particles from lying within the light cones?

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:
$$M_c = f \frac{r_s}{r_1} \sqrt{ \frac{e^{- \frac{r_1}{r_0}}}{G}}$$

$$r_1 < r_0$$

$$r_{c} = \frac{2GM_c}{c^2}$$

Chandresekhar Criterion:
$$r_s <= r_{c}$$

$$r_s <= \frac{2GM_c}{c^2}$$

$$M_{ch} = \frac{r_c c^2}{2G}$$

Classical Chandresekhar-Yukawa Mass Limit:
$$M_c = M_{ch}$$

$$\frac{r_c c^2}{2G} = f \frac{r_s}{r_1} \sqrt{ \frac{e^{- \frac{r_1}{r_0}}}{G}}$$

$$r_s = r_c$$

$$\frac{c^2}{2G} = \frac{f}{r_1} \sqrt{ \frac{e^{- \frac{r_1}{r_0}}}{G}}$$

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

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

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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?

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 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.

Gravity Gyruss...

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

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

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

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

Reference:

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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: