Does the gravitational rate of acceleration increase within a planet?

[A.T.]

I don't believe we will ever reach the extreme density of a black hole.

Why don't you simply write down the formula for density as function of radius that you have in mind?

 

[DaveC426913]

This corresponds to a gravitational acceleration of about 10.7 m/s2 (which is comparable to the gravity at the surface of Saturn!). For comparison, the gravitational acceleration at Earth’s surface is 9.81 m/s2.

Saturn may be physically large but it is not very dense. Given a sufficiently large bathtub, it would float.
I weigh 85kg. On Saturn, I would only weigh 8kg more.

 

[jbriggs444]

I don't believe we will ever reach the extreme density of a black hole.

The idea that black holes have a density at all is problematic. You could divide a black hole mass by $\frac{4}{3}\pi r^3$ where r is its Schwarzschild radius. But this turns out not to be a constant. The larger the hole, the lower the "density" in this sense.

You could consider the local density in the interior of a black hole. But black holes are "vacuum solutions". They are vacuum everywhere. Zero density everywhere. There is no mass anywhere. Just space-time curvature.

You could consider what happens as one gets closer and closer to the singularity. But the geometry of a black hole is strange. Its interior volume is infinite. That $\frac{4}{3}\pi r^3$ formula works for Euclidean geometry, not for the curved pseudo-Riemannian manifold of the Schwarzschild solution.

 

[berkeman]

Thread is closed for Moderation...

 

[PeterDonis]

To the extent I can discern a coherent question that the OP is asking, it appears to be answered.

Thread will remain closed.