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Consider a spherical body of uniform density $\rho$ and initial radius R. You can imagine this body containing another sphere of radius R/2 which touches the center and the periphery of the larger sphere at point P. The smaller sphere has 8 times less mass, since the mass goes as the radius cubed.

If you let the big sphere collapse gravitationally along with the smaller one, keeping the density uniform, the whole thing just shrinks proportionally. The Schwarzschild radius is proportional to the mass, so $R_S= 2GM/c^2$ for the larger mass, and for the smaller sphere $r_S= 2GM/8c^2$, one eighth as big. So when the large mass collapses, the smaller one hasn’t.

It follows that the smaller sphere can still communicate with things outside, but the larger sphere should prevent it from doing so. The outgoing world lines at P due to the smaller sphere must be trapped by the spacetime effects of the residual portion ie, the portion represented by the larger sphere minus the smaller one.It seems that the remaining larger irregular shaped mass has a greater attractive power than the regular shape of greater mass at specific points like P.Is it really so?

For a sphere of a larger fraction of the size, say 3/5R, which touches the boundary of the larger sphere at some point and includes the center [of the larger sphere, the smaller Schwarzschild radius is about .2 of the larger Schwarzschild radius.

When the larger sphere collapses the smaller one has not collapsed---it has escaping null world lines (light rays) that can go in the outward direction.The smaller sphere is not supposed to have a singularity on its own.But it contains the singularity of the bigger mass , though not at its center.Is the singularity, [of the larger sphere], produced by the effect of the residual portion?

Related question: Can we conclude solely on the basis of these “Experiments’ that different parts of the body can exchange signals after it has collapsed? [QM effects are not being considered in this problem]

Consider a spherical body of uniform density $\rho$ and initial radius R. You can imagine this body containing another sphere of radius R/2 which touches the center and the periphery of the larger sphere. The smaller sphere has 8 times less mass, since the mass goes as the radius cubed.

If you let the big sphere collapse gravitationally along with the smaller one, keeping the density uniform, the whole thing just shrinks proportionally. The Schwarzschild radius is proportional to the mass, so $R_S= 2GM/c^2$ for the larger mass, and for the smaller sphere $r_S= 2GM/8c^2$, one eigth as big. So when the large mass collapses, the smaller one hasn’t.

It follows that the smaller sphere can still communicate with things outside, but the larger sphere should prevent it from doing so. The outgoing world lines at P due to the smaller sphere must be trapped by the spacetime effects of the residual portion ie, the portion represented by the larger sphere minus the smaller one.It seems that the remaining larger irregular shaped mass has a greater attractive power than the regular shape of greater mass at specific points like P.Is it really so?

For a sphere of a larger fraction of the size, say 3/5R, which touches the boundary of the larger sphere at some point and includes the center [of the larger sphere, the smaller Schwarzschild radius is about .2 of the larger Schwarzschild radius.

When the larger sphere collapses the smaller one has not collapsed---it has world lines in the outward direction.The smaller sphere is not supposed to have a singularity on its own.But it contains the singularity of the bigger mass , though not at its center.Is the singularity, [of the larger sphere], produced by the effect of the residual portion?

Related question: Can we conclude solely on the basis of these “Experiments’ that different parts of the body can exchange signals after it has collapsed? [QM effects are not being considered in this problem]

Consider a spherical body of uniform density $\rho$ and initial radius R. You can imagine this body containing another sphere of radius R/2 which touches the center and the periphery of the larger sphere. The smaller sphere has 8 times less mass, since the mass goes as the radius cubed.

If you let the big sphere collapse gravitationally along with the smaller one, keeping the density uniform, the whole thing just shrinks proportionally. The Schwarzschild radius is proportional to the mass, so $R_S= 2GM/c^2$ for the larger mass, and for the smaller sphere $r_S= 2GM/8c^2$, one eigth as big. So when the large mass collapses, the smaller one hasn’t.

It follows that the smaller sphere can still communicate with things outside, but the larger sphere should prevent it from doing so. The outgoing world lines at P due to the smaller sphere must be trapped by the spacetime effects of the residual portion ie, the portion represented by the larger sphere minus the smaller one.It seems that the remaining larger irregular shaped mass has a greater attractive power than the regular shape of greater mass at specific points like P.Is it really so?

For a sphere of a larger fraction of the size, say 3/5R, which touches the boundary of the larger sphere at some point and includes the center [of the larger sphere, the smaller Schwarzschild radius is about .2 of the larger Schwarzschild radius.

When the larger sphere collapses the smaller one has not collapsed---it has world lines in the outward direction.The smaller sphere is not supposed to have a singularity on its own.But it contains the singularity of the bigger mass , though not at its center.Is the singularity, [of the larger sphere], produced by the effect of the residual portion?

Related question: Can we conclude solely on the basis of these “Experiments’ that different parts of the body can exchange signals after it has collapsed? [QM effects are not being considered in this problem]

Consider a spherical body of uniform density $\rho$ and initial radius R. You can imagine this body containing another sphere of radius R/2 which touches the center and the periphery of the larger sphere at point P. The smaller sphere has 8 times less mass, since the mass goes as the radius cubed.

If you let the big sphere collapse gravitationally along with the smaller one, keeping the density uniform, the whole thing just shrinks proportionally. The Schwarzschild radius is proportional to the mass, so $R_S= 2GM/c^2$ for the larger mass, and for the smaller sphere $r_S= 2GM/8c^2$, one eighth as big. So when the large mass collapses, the smaller one hasn’t.

It follows that the smaller sphere can still communicate with things outside, but the larger sphere should prevent it from doing so. The outgoing world lines at P due to the smaller sphere must be trapped by the spacetime effects of the residual portion ie, the portion represented by the larger sphere minus the smaller one.It seems that the remaining larger irregular shaped mass has a greater attractive power than the regular shape of greater mass at specific points like P.Is it really so?

For a sphere of a larger fraction of the size, say 3/5R, which touches the boundary of the larger sphere at some point and includes the center [of the larger sphere, the smaller Schwarzschild radius is about .2 of the larger Schwarzschild radius.

When the larger sphere collapses the smaller one has not collapsed---it has escaping null world lines (light rays) that can go in the outward direction.The smaller sphere is not supposed to have a singularity on its own.But it contains the singularity of the bigger mass , though not at its center.Is the singularity, [of the larger sphere], produced by the effect of the residual portion?

Related question: Can we conclude solely on the basis of these “Experiments’ that different parts of the body can exchange signals after it has collapsed? [QM effects are not being considered in this problem]

We consider a spherical body of uniform density $\rho$ and initial radius R. Inside this body we mentally consider another spherical mass of radius R/2 which touches the center and the periphery of the larger mass. Suppose it touches the boundary of the larger sphere at P.

Mass of the larger sphere=M

Mass of the smaller sphere =m

$$M=\frac{4}{3}\pi R^3\rho$$ $$m=\frac{4}{3}\pi(R/2)^3\rho$$

Therefore,

$$m=M/8$$

Now lets consider the collapse of the larger sphere along with the smaller one, density always remaining uniform but increasing during the collapse. The smaller sphere always has a radius =half the larger one. It touches the center and the surface of the larger mass at all points of time.

Schwarzschild’s radius for the larger sphere $R_S= 2GM/c^2$

Schwarzschild’s radius for the smaller sphere $r_S= 2GM/8c^2$

Therefore, $$r_S=1/8 \times R_S$$ When the larger sphere has collapsed [or when it is about to collapse] the smaller one hasn’t since its radius is always half that of the larger sphere!

Since the smaller sphere touches the boundary of the larger one[at P], it has the capability of communicating with the external world, though the larger sphere should prevent it or prohibit it from doing so. But we may argue in the following manner: The outgoing world lines at P due to the smaller sphere get canceled by the spacetime effects of the residual portion ie, the portion represented by the larger sphere minus the smaller one.It seems intuitively ,at least, that irregular shapes have greater attractive power than regular shapes of greater mass at specific points like P.Is it really so?

We may repeat the same “experiment” with a mass of radius 3/5R which touches the boundary of the larger sphere at some point and includes the center [of the larger sphere]

Schwarzschild Radius for the larger mass:$R_{S}=\frac{2GM}{c^2}$

Schwarzschild Radius for the smaller mass:$r_{S}=\frac{2GM}{c^2}\times 27/125$

That is,

$ r_{S}=\frac{27}{125}\times R_{S}$

When the larger sphere collapses[density remaining uniform as it collapses] the smaller one has not collapsed---it has world lines in the outward direction.The smaller sphere is not supposed to have a singularity on its own.But it contains the singularity of the bigger mass , though not at its center.Is the singularity, [of the larger sphere], produced by the effect of the residual portion?

Allied Query: Can we conclude solely on the basis of these “Experiments’ that different parts of the body can exchange signals after it has collapsed? [QM effects are not being considered in this problem]

Consider a spherical body of uniform density $\rho$ and initial radius R. You can imagine this body containing another sphere of radius R/2 which touches the center and the periphery of the larger sphere. The smaller sphere has 8 times less mass, since the mass goes as the radius cubed.

If you let the big sphere collapse gravitationally along with the smaller one, keeping the density uniform, the whole thing just shrinks proportionally. The Schwarzschild radius is proportional to the mass, so $R_S= 2GM/c^2$ for the larger mass, and for the smaller sphere $r_S= 2GM/8c^2$, one eigth as big. So when the large mass collapses, the smaller one hasn’t.

It follows that the smaller sphere can still communicate with things outside, but the larger sphere should prevent it from doing so. The outgoing world lines at P due to the smaller sphere must be trapped by the spacetime effects of the residual portion ie, the portion represented by the larger sphere minus the smaller one.It seems that the remaining larger irregular shaped mass has a greater attractive power than the regular shape of greater mass at specific points like P.Is it really so?

For a sphere of a larger fraction of the size, say 3/5R, which touches the boundary of the larger sphere at some point and includes the center [of the larger sphere, the smaller Schwarzschild radius is about .2 of the larger Schwarzschild radius.

When the larger sphere collapses the smaller one has not collapsed---it has world lines in the outward direction.The smaller sphere is not supposed to have a singularity on its own.But it contains the singularity of the bigger mass , though not at its center.Is the singularity, [of the larger sphere], produced by the effect of the residual portion?

Related question: Can we conclude solely on the basis of these “Experiments’ that different parts of the body can exchange signals after it has collapsed? [QM effects are not being considered in this problem]