# Thread: Distances inside black holes

1. ## Distances inside black holes

Black holes have been popularly described as a gravity well which bends space to infinity at their center. But wouldn't then its inner material, its mass, be disributed in that gravity well of curved space? Wouldn't much of it be very far away (millions of light years?) from the surface of the black hole, so that it has little effect on its surface gravity?

If we drill us down towards the center of the Earth, gravity will increase at first! Because we get closer to high density materials in the core, which compensates for more than the increasing pull back up from the lighter material between us and the surface. The further away from the surface dense matter is located, the less effect does it have on the surface. Some of the mass of a Black Hole should be in its center, curved infinitely far away, and have no gravitational effect on the surface.

https://en.wikipedia.org/wiki/Gravity_of_Earth#Depth

2. Originally Posted by Zwart Gat
Black holes have been popularly described as a gravity well which bends space to infinity at their center.
Popularly, but not scientifically.

But wouldn't then its inner material, its mass, be disributed in that gravity well of curved space? Wouldn't much of it be very far away (millions of light years?) from the surface of the black hole, so that it has little effect on its surface gravity?
There's no way to know what goes on at the "surface" of a BH's central mass, since it lies within the event horizon which marks the limits of our observation.

If we drill us down towards the center of the Earth, gravity will increase at first! Because we get closer to high density materials in the core, which compensates for more than the increasing pull back up from the lighter material between us and the surface. The further away from the surface dense matter is located, the less effect does it have on the surface. Some of the mass of a Black Hole should be in its center, curved infinitely far away, and have no gravitational effect on the surface.
Gravity is curved space. The greater the curvature, the greater the gravity field.

3. Originally Posted by Noclevername
Gravity is curved space. The greater the curvature, the greater the gravity field.

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The measurements taken inside a black hole and outside are notoriously hard to reconcile if you use the wrong coordinate systems or try to swap back and forth without carefully defining your units, metrics of distance and so on. A simple way to think of it is that what matters to us is the amount of mass and our measurement of the volume in which it is contained. So we can 'see' the event horizon and measure it using our coordinates. We know the mass it has to have from the mass of the progenitor. And these are what we need to work out gravitational effects.

Another way to think about it is to invoke causality. The event horizon marks the boundary at which something becomes causally disconnected from us. Nothing it does after that matters, even if it did fall away to infinity in its own frame the 'signal' that it had done that would never get to us.

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Originally Posted by Zwart Gat
Black holes have been popularly described as a gravity well which bends space to infinity at their center. But wouldn't then its inner material, its mass, be disributed in that gravity well of curved space? Wouldn't much of it be very far away (millions of light years?) from the surface of the black hole, so that it has little effect on its surface gravity?

If we drill us down towards the center of the Earth, gravity will increase at first! Because we get closer to high density materials in the core, which compensates for more than the increasing pull back up from the lighter material between us and the surface. The further away from the surface dense matter is located, the less effect does it have on the surface. Some of the mass of a Black Hole should be in its center, curved infinitely far away, and have no gravitational effect on the surface.

https://en.wikipedia.org/wiki/Gravity_of_Earth#Depth
Your argument has a flaw and that is that it fails to recognize the shell theorem. It doesn't matter how far inside the surface of a sphere the mass is located, it will still have the same gravitational effect on you being at the surface of that sphere.

You might expect this to still be different if the mass is actually infinitely far away to the center (and there are certainly coordinates in which that happens) but you have to recognize that in those coordinates the spherical mass you started with then also had infinite volume and if you take the limit where you let the size of massive sphere go to zero (and thus infinitely far away) it still works out. The effects of increasing density and increasing distance will cancel.

6. Originally Posted by Zwart Gat
But wouldn't then its inner material, its mass, be disributed in that gravity well of curved space? Wouldn't much of it be very far away (millions of light years?) from the surface of the black hole, so that it has little effect on its surface gravity?
No. You might say that the mass of a black hole is maximally "undistributed."

Our own Sun's gravity well obviously reaches Earth and beyond, but its mass is confined to a spherical volume of about 1.4 million km. The distance from the Sun to Earth is more like 150 million km.

The supermassive black hole at the center of the Milky Way galaxy has a mass of about 4 million solar masses, but a radius of only around 6.25 lighthours.

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Originally Posted by Zwart Gat
Black holes have been popularly described as a gravity well which bends space to infinity at their center. But wouldn't then its inner material, its mass, be disributed in that gravity well of curved space? Wouldn't much of it be very far away (millions of light years?) from the surface of the black hole, so that it has little effect on its surface gravity?

If we drill us down towards the center of the Earth, gravity will increase at first! Because we get closer to high density materials in the core, which compensates for more than the increasing pull back up from the lighter material between us and the surface. The further away from the surface dense matter is located, the less effect does it have on the surface. Some of the mass of a Black Hole should be in its center, curved infinitely far away, and have no gravitational effect on the surface.

https://en.wikipedia.org/wiki/Gravity_of_Earth#Depth
The space/time curvature at the center of a BH [the singularity] is probably not infinite.
It's just that at the quantum level where the singularity is, our models and theories break down.
In reality below where our theories and models break down, there is a surface of sorts, just at this time, it is at a scale and level which we are unable to observe.

Also the BH's total mass is at the singularity, and it cannot "communicate" with the surface gravity [Event Horizon] as the escape velocity at that point is greater then "c"
The BH and the gravitational space/time curvature is a result of the property of non-linearity of gravity/space/time as I understand it.
The concept of the "Eternal BH" is an example of this.
see....
http://scienceworld.wolfram.com/phys...BlackHole.html

Remember all the mass of the BH is at the center singularity....the rest is just critically curved space/time, ignoring any incoming mass of course.

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My understanding is that the "depth" of the "gravity well" of a
black hole increases with time, and without limit. So it is not
infinite but is headed in that direction.

However, the mechanism described in the first post, in which
"normal" massive bodies like the Earth have smaller net
downward "force" of gravity the closer you get to the center
of the mass, would be interesting to try to apply in the case
of a black hole. I can't imagine what the result might be.

I don't know how to reconcile the depth of the gravity well
with my further understanding that everything falling into
a black hole is pulled apart in the radial direction, including
the matter which originally forms the black hole. Everything
lower down is "pulled" harder and falls faster than everything
that is higher up, and the gradient just keeps increasing as
it falls.

-- Jeff, in Minneapolis

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Originally Posted by Jeff Root
My understanding is that the "depth" of the "gravity well" of a
black hole increases with time, and without limit. So it is not
infinite but is headed in that direction.
The central singularity is reached in finite proper time, so if you have coordinates in which it is infinitely far away then the depth is infinite in finite time, if you have coordinates in which it is a finite distance away then the depth is finite in finite time. In either case, it is static after finite time, it doesn't "keep increasing".

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Originally Posted by caveman1917
Originally Posted by Jeff Root
My understanding is that the "depth" of the "gravity well" of a
black hole increases with time, and without limit. So it is not
infinite but is headed in that direction.
The central singularity is reached in finite proper time, ...
Agreed. Reached in finite proper time by anything falling in.
And that finite time is quite short.

Originally Posted by caveman1917
... so if you have coordinates in which it is infinitely far
away then the depth is infinite in finite time, ...
I don't have such coordinates. The depth would only be
infinite after infinite time... meaning never.

Originally Posted by caveman1917
... if you have coordinates in which it is a finite distance
away then the depth is finite in finite time. ...
Yes.

Originally Posted by caveman1917
... In either case, it is static after finite time, it doesn't
"keep increasing".
My understanding is still that it does keep increasing.
There is nothing to stop the matter's fall. It just keeps
on falling endlessly. That endless fall is a short finite
time by the faller's clock, though.

-- Jeff, in Minneapolis

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Originally Posted by Jeff Root
I don't have such coordinates. The depth would only be
infinite after infinite time... meaning never.
No it wouldn't, which you can simply see because schwarzschild is a static spacetime - it doesn't change over time so neither can the depth increase over time.

My understanding is still that it does keep increasing.
There is nothing to stop the matter's fall. It just keeps
on falling endlessly. That endless fall is a short finite
time by the faller's clock, though.
How is the fall endless if it ends after a short finite time?
Last edited by caveman1917; 2013-Apr-18 at 12:53 PM.