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More Confused Than Usual: Black Holes

Was thinking about that huge black hole at the heart of M87, and that got me thinking about time dilation due to gravity and event horizons. "Cook-booking" it, the equation for escape velocity is v = Squareroot(2GM/r), where G is the gravitational constant 6.67408 x 10^-11, M the mass in kilograms of the object you're trying to escape, and r is the starting distance in meters from the center of the mass M. The escape velocity at the event horizon is the speed of light, c, so solving for r:

c = Squareroot (2GM/r); c^2=2GM/r; r = 2GM/c^2

That's straight-forward. The confusion starts with time dilation due to gravity. If you assume an observer infinitely away from the source, the time he observes happening near a mass is To = T*squareroot(1-2GM/rc^2). So, our observer, looking at a clock on the surface of the earth, would see it move 0.9999 times as fast as their own. All well and good. But applying this to black holes, well ...

We can simplify things by noticing that 2GM/c^2 is the formula for an event horizon, and substitute e.h. for that. That gives us To = T*squareroot[1-(e.v./r)]. When r = e.v., we have T*squareroot([1-1]) = T*squareroot(0) = T * 0 = 0. Time seems to stop at the event horizon for our observer. Watching an astronaut move toward the event horizon, our observer sees him red shift further and further until he vanishes. Of course, the poor soul approaching the event horizon won't notice it, but it will seem to him like the entire universe is on fast forward, blue shifting until it seems to disappear.

Now, here's where I get more confused than usual. Both observers are witnessing things concurrently, with one slowing in respect to the universe, and the universe speeding faster to the other. That's no different that an object moving near the speed of light. But here we are on the event horizon. In respect to the universe, the astronaut never crosses, and the astronaut never realizes it. So, if nothing can actually pass an event horizon, how to black holes accumulate mass?

This is my confusion. Obviously black holes accumulate mass and grow. The weird thing going through my mind is that as mass accumulates along the event horizon, the event horizon expands. The astronaut doesn't cross the event horizon; the event horizon eventually engulfs him. And that ... well, I don't know. I'm cook-booking this from a couple of canned equations; nothing more.

After that point, it involves imaginary numbers. And while that's simple enough - call the square root of -1 i, multiply it by squareroot[e.v./(r-1)], and call it a day - have no idea what that would mean. Cook-booking it only goes so far.

So, what am I missing here?
 
Watching an astronaut move toward the event horizon, our observer sees him red shift further and further until he vanishes. Of course, the poor soul approaching the event horizon won't notice it, but it will seem to him like the entire universe is on fast forward, blue shifting until it seems to disappear.

Now, here's where I get more confused than usual. Both observers are witnessing things concurrently, with one slowing in respect to the universe, and the universe speeding faster to the other. That's no different that an object moving near the speed of light. But here we are on the event horizon. In respect to the universe, the astronaut never crosses, and the astronaut never realizes it.



So, what am I missing here?

For the astronaut, and all of us, it boils down to the simplest form:

 
Sounds like the riddle where you start off some distance away from a wall. Then move halfway closer to it. Then move halfway closer again. Halfway closer again. And again, ... You are moving forward, getting infinitesimally closer to the wall but never reaching it. While gravity/electrical forces between body and wall intensify.
 
If the event horizon is static, yes. But the event horizon is just a zone, the point where light can no longer escape. Once the event horizon expands past the matter, the situation changes. Disregarding the square root of -1, it looks like time dilation would start moving the other way. Maybe our astronaut would see things slow and blue shift, then speed up again as the event horizon passed him? Just confused on how these things actually would grow due to time dilation.
 

TexLaw

Fussy Evil Genius
So, what am I missing here?

Essentially, you're missing that classical physics and general relativity completely break down at the event horizon. Our current state of physics (i.e., general relativity) has no capability to describe what actually happens at the event horizon.

For example, general relativity says that, at the event horizon, spacetime closes completely around the infinitely dense singularity, but that's only because general relativity loses all relevance at that point. We know that what general relativity predicts at and inside the event horizon is not correct. We know full well that whatever might be at or inside the event horizon cannot be of infinite density, because infinite density would mean infinite gravity, and that's not what it going on or we'd all be in the black hole. This is a case where "infinite" does not mean "unlimited" or "never ending." Instead, this is where we just cannot describe what's going on, so general relativity just throws up its hands and says "infinite."

In respect to the universe, the astronaut never crosses, and the astronaut never realizes it. So, if nothing can actually pass an event horizon, how to black holes accumulate mass?

The time dilation effect may slow things down tremendously, but not to the point that time completely stops from the observer's point of view. That would require actually unlimited density, and we know that's not the case. The astronaut will, eventually, cross the event horizon, and the observer would see the astronaut's image red-shift further and further until it eventually faded completely away.
 
Black holes - the ultimate enigma.
Imaginary numbers, infinite density, a "place" where our established physical laws don't apply. How do we even begin to understand such a thing?

The topic makes for some interesting movie material (Disney's 1979 "The Black Hole" and the more recent "Interstellar", which had great visuals but a abysmally disappointing climax), but otherwise doesn't really help me in daily life.
 
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Essentially, you're missing that classical physics and general relativity completely break down at the event horizon. Our current state of physics (i.e., general relativity) has no capability to describe what actually happens at the event horizon.

For example, general relativity says that, at the event horizon, spacetime closes completely around the infinitely dense singularity, but that's only because general relativity loses all relevance at that point. We know that what general relativity predicts at and inside the event horizon is not correct. We know full well that whatever might be at or inside the event horizon cannot be of infinite density, because infinite density would mean infinite gravity, and that's not what it going on or we'd all be in the black hole. This is a case where "infinite" does not mean "unlimited" or "never ending." Instead, this is where we just cannot describe what's going on, so general relativity just throws up its hands and says "infinite."



The time dilation effect may slow things down tremendously, but not to the point that time completely stops from the observer's point of view. That would require actually unlimited density, and we know that's not the case. The astronaut will, eventually, cross the event horizon, and the observer would see the astronaut's image red-shift further and further until it eventually faded completely away.


I found Einstein's own book on explaining Special Relativity and General Relativity on Project Gutenberg, and will be giving it a look. I had this in a physics class back in the day, but it was more Special Relativity, which isn't all that difficult to grasp. I'm not sure I buy infinite density, though I think the argument goes that gravity starts to overwhelm the other fundamental forces, and you get something denser than neutronium that doesn't stop collapsing.

Stopping time gets into an "close enough" situation. If the universe ends with someone sitting just about on an event horizon, time's close enough to stopped for that poor soul - assuming the black hole doesn't evaporate out from under him.

I don't know. Wish I had a better grasp of this stuff.
 
Black holes - the ultimate enigma.
Imaginary numbers, infinite density, a "place" where our established physical laws don't apply. How do we even begin to understand such a thing?

The topic makes for some interesting movie material (Disney's 1979 "The Black Hole" and the more recent "Interstellar", which had great visuals but a abysmally disappointing climax), but otherwise doesn't really help me in daily life.

Had a "Doh!" moment this evening realizing there's a way around imaginary numbers by simply squaring both sides of the equation. You end up with two possible answers, but no imaginary numbers.
 
Essentially, you're missing that classical physics and general relativity completely break down at the event horizon. Our current state of physics (i.e., general relativity) has no capability to describe what actually happens at the event horizon.

For example, general relativity says that, at the event horizon, spacetime closes completely around the infinitely dense singularity, but that's only because general relativity loses all relevance at that point. We know that what general relativity predicts at and inside the event horizon is not correct. We know full well that whatever might be at or inside the event horizon cannot be of infinite density, because infinite density would mean infinite gravity, and that's not what it going on or we'd all be in the black hole. This is a case where "infinite" does not mean "unlimited" or "never ending." Instead, this is where we just cannot describe what's going on, so general relativity just throws up its hands and says "infinite."



The time dilation effect may slow things down tremendously, but not to the point that time completely stops from the observer's point of view. That would require actually unlimited density, and we know that's not the case. The astronaut will, eventually, cross the event horizon, and the observer would see the astronaut's image red-shift further and further until it eventually faded completely away.

It doesn't necessarily break down at the event horizon. It breaks down at the singularity. You just can't observe what's going on beyond the event horizon so in that sense you could describe that as "breaking down" I suppose.

Relativity breaks down at the quantum level as there is no quantum gravity theory and therefore the math of relativity breaks down when infinities are invoked.
 
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Was thinking about that huge black hole at the heart of M87, and that got me thinking about time dilation due to gravity and event horizons. "Cook-booking" it, the equation for escape velocity is v = Squareroot(2GM/r), where G is the gravitational constant 6.67408 x 10^-11, M the mass in kilograms of the object you're trying to escape, and r is the starting distance in meters from the center of the mass M. The escape velocity at the event horizon is the speed of light, c, so solving for r:

c = Squareroot (2GM/r); c^2=2GM/r; r = 2GM/c^2

That's straight-forward. The confusion starts with time dilation due to gravity. If you assume an observer infinitely away from the source, the time he observes happening near a mass is To = T*squareroot(1-2GM/rc^2). So, our observer, looking at a clock on the surface of the earth, would see it move 0.9999 times as fast as their own. All well and good. But applying this to black holes, well ...

We can simplify things by noticing that 2GM/c^2 is the formula for an event horizon, and substitute e.h. for that. That gives us To = T*squareroot[1-(e.v./r)]. When r = e.v., we have T*squareroot([1-1]) = T*squareroot(0) = T * 0 = 0. Time seems to stop at the event horizon for our observer. Watching an astronaut move toward the event horizon, our observer sees him red shift further and further until he vanishes. Of course, the poor soul approaching the event horizon won't notice it, but it will seem to him like the entire universe is on fast forward, blue shifting until it seems to disappear.

Now, here's where I get more confused than usual. Both observers are witnessing things concurrently, with one slowing in respect to the universe, and the universe speeding faster to the other. That's no different that an object moving near the speed of light. But here we are on the event horizon. In respect to the universe, the astronaut never crosses, and the astronaut never realizes it. So, if nothing can actually pass an event horizon, how to black holes accumulate mass?

This is my confusion. Obviously black holes accumulate mass and grow. The weird thing going through my mind is that as mass accumulates along the event horizon, the event horizon expands. The astronaut doesn't cross the event horizon; the event horizon eventually engulfs him. And that ... well, I don't know. I'm cook-booking this from a couple of canned equations; nothing more.

After that point, it involves imaginary numbers. And while that's simple enough - call the square root of -1 i, multiply it by squareroot[e.v./(r-1)], and call it a day - have no idea what that would mean. Cook-booking it only goes so far.

So, what am I missing here?

What you are missing is that the astronaut does pass the event horizon. What the observer sees is not relevant concerning what is actually happening to the astronaut.
 
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Watching an astronaut move toward the event horizon, our observer sees him red shift further and further until he vanishes. Of course, the poor soul approaching the event horizon won't notice it, but it will seem to him like the entire universe is on fast forward, blue shifting until it seems to disappear.
Then there's the notion of a microsingularity, which is a very tiny black hole with the mass of, say, a Big Mac.
IIRC, it could pass right through the astronaut without him even being aware of it.
 
What you are missing is that the astronaut does pass the event horizon. What the observer sees is not relevant concerning what is actually happening to the astronaut.

Remember, this is happening concurrently. The distant observer sees time slow at the event horizon; the observer at the event horizon sees time speed up for the distant observer, and both are actually happening from the perspective of the other. A good example is time dilation in atomic clocks at different altitudes. If an observer on the ground only perceived time as slowing for the clock at a higher altitude, the clocks would show the same time when brought together, but they don't. Time has sped up for one simply by being further from the earth's mass.

Thus, our distant observer is simply seeing events happen slower on the event horizon than the observer actually there, but both are perceiving what is happening "now," except "now" goes by a lot slower for the astronaut.
 
Math doesn’t explain everything.

What is the mathematical equation of eating an apple?

Math isn't so much an explanation as it is a model. The classical model is a little off for Mercury's orbit, so that means the model isn't exactly what's going on. General Relativity proved a better model.

So, we use the mathematical models of General Relativity to predict things like time dilation at different altitudes. Where it breaks down, that means either it's not exactly modeling things correctly, or we're not grasping it correctly. Since the call that it's not modeling things correctly is way above my pay grade, I go with not grasping what's going on. That's usually the case with such things.:wink2:
 
Remember, this is happening concurrently. The distant observer sees time slow at the event horizon; the observer at the event horizon sees time speed up for the distant observer, and both are actually happening from the perspective of the other. A good example is time dilation in atomic clocks at different altitudes. If an observer on the ground only perceived time as slowing for the clock at a higher altitude, the clocks would show the same time when brought together, but they don't. Time has sped up for one simply by being further from the earth's mass.

Thus, our distant observer is simply seeing events happen slower on the event horizon than the observer actually there, but both are perceiving what is happening "now," except "now" goes by a lot slower for the astronaut.
These comments don't address my comments. The astronaut does go past the event horizon.
 
The point is when? Time at the event horizon is slower than compared to the distant observer. Unless the event horizon itself moves, the astronaut gets ever closer, but never crosses, and the astronaut never knows it. The universe could end, and he'd never know it. It's the time dilation issue.

OTOH, if the event horizon moves as mass accumulates along the event horizon, then it crosses the astronaut rather than the astronaut crosses it. Time dilation is then no longer an issue.
 
From Wikipedia:

Fuzzball theory replaces the singularity at the heart of a black hole by positing that the entire region within the black hole's event horizon is actually a ball of strings, which are advanced as the ultimate building blocks of matter and energy. Strings are thought to be bundles of energy vibrating in complex ways in both the three physical dimensions of space as well as in compact directions—extra dimensions interwoven in the quantum foam (also known as spacetime foam).

abstractions_be45b04f30581edd9d3595e5659a741e.jpg
 

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