neutron stars and colour force

[kurious]

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.

[selfAdjoint]

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]

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

[Orion1]

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?

[zefram_c]

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.

[Rothiemurchus]

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

[Orion1]

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

Classical GR Chandresekhar Radius:
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?

[Orion1]

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?

[zefram_c]

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:
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.

[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)

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:
http://super.colorado.edu/~michaele/Lambda/gr.html

[Orion1]

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


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