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Comment by cgriswald | Hacker News Reader

Each mass creates a “dimple” on the cellophane but because they have different density, the shape of that dimple is different. The less dense object has a shallower cone. The infinitely dense object has a steeper one.

If you’re five feet from the surface of the sun you’re hundreds of thousands of miles away from its center of mass. If you’re five feet away from the “surface” of a solar mass black hole you’re just a couple of miles away from the center of mass.

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Except this is not entirely true.

The shape of gravitational field only differs within the body. The shape outside of the perfectly spherical body will be exactly the same regardless of how the mass is distributed (whether it is all on the surface or all in the middle of it).

Or in other words, if you are on the surface of the sun, you will feel exactly the same acceleration as if entire mass of the sun was concentrated in its center.

The only time you feel the difference is if you dip into the sun. As you go deeper and deeper, the pull from all the mass that is further from the center than you are will perfectly nullify each other. As you go deeper and deeper into the sun you will feel less acceleration.

So yea, this lets you equate standing on the surface of a given star of X radius, with hovering the same X distance away from a neutron star or black hole of the same mass.

The takeaway is that the cellophane dimple is more warped around the center point, but if, say, our Sun were to suddenly turn into a black hole it wouldn't change anything about our orbit.

Nitpick: you will not feel acceleration in a freefall.

You’ll feel the tides, however.

These analogies always fall apart for me because you'll be burnt to nothing long before you reach the surface of the sun.

Your analogy falls apart, too. Sun does not have a surface to be reached. It just sort of gets more and more dense and that's all.

What is "feeling"? If my senses can register changing spectra of the stars around me then yes, I will "feel" the acceleration.

I didn't think you could accelerate at all in a freefall (which is why you wouldn't feel it), you are just following a geodesic

However, when you're 5 miles away from the surface of a black hole, you would be inside the sun, so the shape will be different. We are not comparing equal distances from the center of mass, but equal distances from the surface; which are different distances! Only if you are the same distance from the sun as from a black hole, what you say is correct. But then you will be much farther away from the black hole than in this example.

Distance from the body I have defined as distance from its center.

Black hole does not have a surface. At least not that we know of. Event horizon is a surface, but it is not the surface of the BH in conventional sense. If you were falling into BH nothing special would happen as you crossed event horizon.

And neither does the Sun. Just like Earth's atmosphere, we can only talk about some arbitrary altitudes or pressures, but reality is that the atmosphere of the Sun or Earth does not have any firm beginning or end. And Sun is all atmosphere.

Since the speed of light is a constant, mass increases towards infinity as it approaches the speed of light, and time slows for the matter relative to matter with lesser velocity, does that mean that matter accelerating towards a black hole increases the mass in the region and further increases the magnitude of the effect on the spacetime curve?

Is the mass of the black hole perpetually "falling" through spacetime at near the speed of light?

Would the region around an "active" black hole appear more massive when it is consuming matter vs existing in a vacuum?

A big object going really fast would be almost stopped in time, while at the same moment be almost infinitely massive which is increasing the gravitational effect. The combination of these effects is what makes such a big "dent" in spacetime?

Exactly.

Also, if you are hundreds of thousands of miles from the center of mass of the sun, you'd feel the same force from gravity as if you were the same distance from the center of mass of a black hole (with the same mass).

Far away, the curvature of spacetime is the same, it's just that with black holes you can get waaaay closer to the center of mass whilst still being outside of it.

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