Can you fall into a non-accreting back hole?

[kamenjar]

Let's say I was point-like but have mass (not a photon) and I wanted to "go into" a black hole's event horizon, just to see how it was like... :)

I am not sure if it would be possible because maybe the black hole would evaporate before I would reach the event horizon, and here's what I'm thinking...
- As I approach the black hose, I am experiencing a large time dilation due to its gravity.
- This increasing time dilation causes "me" to reach the event horizon longer and longer. From my reference frame, I see the universe age more and more.
- As the universe ages, the black hole evaporates faster. It has no mass to feed on, so it just continues to evaporate.
- If I wanted to "accelerate" myself in order to reach the event horizon "sooner", my time dilation would just add to the problem and the black hole would evaporate even faster with respect to myself.

So I never reach the black hole's event horizon, or I do, or I do or don't, depending on the original size of it?

I think that this can be solved by equations only, but I doubt I'll understand them, so I guess, I am just interested in a final answer. Any brave empiricists? :)

 

[pervect]

While there is a lot we don't know about the internal structure of black holes due to realistic collapse, having them evaporate before you fall in isn't in the cards.

For a non-technical reference, see http://cosmology.berkeley.edu/Education/BHfaq.html#q9

Event horizons occur in physics with accelerating observers without black holes - the standard example is the "Rindler horizon" of an observer with a constant proper acceleration. If someone gets in a rocket ship and accelerates away from the Earth at 1g, when he gets to be about 1 light year away, signals from the Earth will no longer be able to reach him. It will look just as if the Earth has fallen behind an event horizon. From the point of view of the observer on the rocketship, in fact it _has_ fallen behind an event horizon. However, while one can argue for thermodynamic reasons that the Earth will eventually evaporate, (even without the sun, it will have a finite temperature, and so have a finite vapor pressure), it won't happen in the matter of the few years.

While _static_ observers hovering above the event horizon do experience large time dilations, it is in large part a consequence of their efforts to avoid being sucked in. Observers who actually fall into a black hole don't experience large time dilations - the total proper time to fall in varies depending on the size of the black hole, but it's very short. From Ted Bunn's FAQ:

How long does the whole process take? Well, of course, it depends on how far away you start from. Let's say you start at rest from a point whose distance from the singularity is ten times the black hole's radius. Then for a million-solar-mass black hole, it takes you about 8 minutes to reach the horizon. Once you've gotten that far, it takes you only another seven seconds to hit the singularity. By the way, this time scales with the size of the black hole, so if you'd jumped into a smaller black hole, your time of death would be that much sooner.

Another useful reference is http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html which also mentions most of the same points.

So - the evaporation may happen, eventually, but it will occur far to late to save you if you're foolish enough to jump into a black hole.

 

[bcrowell]

- This increasing time dilation causes "me" to reach the event horizon longer and longer. From my reference frame, I see the universe age more and more.

Yes, but it takes you a finite time to reach the event horizon by your own clock, and a finite time after that to reach the singularity.

If it was impossible for *you* to fall in before the black hole evaporated out from under you, then the same would be true for any particle accreting onto a non-accreting black hole. Therefore it would be impossible for a black hole to form at all, because no particle could ever be the last particle to accrete. So the question here isn't really whether it's impossible for you to fall into a black hole before it evaporates, it's whether it's impossible for a black hole to form in the first place, due to quantum effects. That's a possibility that's been seriously proposed, but I don't think the mechanism is the one you're suggesting: http://arxiv.org/abs/0902.0346

 

[Passionflower]

Let's say I was point-like but have mass (not a photon) and I wanted to "go into" a black hole's event horizon, just to see how it was like... :)

The simplest term to use is to say that you want to pass the event horizon. The event horizon is a sphere and is two dimensional.

By the way, despite what many people think, it is not that easy to fall into a black hole, if you do not approach the black hole radially you have a good chance of passing it by.

- As I approach the black hole, I am experiencing a large time dilation due to its gravity.

As you approach it you would experience tidal effects but not time dilation. Sure your clock would be running slower if we compare it with some far away clock but for you that would not make any difference. Time would just go one second per second as always.

- This increasing time dilation causes "me" to reach the event horizon longer and longer.

It depends on how you travel, but if we assume radial motion at escape velocity your proper velocity going towards the event horizon will increase the closer you get to it.

From my reference frame I see the universe age more and more.

Again, that also depends on how you travel, again if you travel radially at escape velocity you will see the rest of the universe speed up but you will not, as many people seem to think, see the complete future of the history pass by when you reach the event horizon.

I think that this can be solved by equations only, but I doubt I'll understand them, so I guess, I am just interested in a final answer. Any brave empiricists? :)

Some of the equations are not that hard, for instance your proper velocity in coordinate distance from the event horizon will be (we assume radial motion at escape velocity and a Schwarzschild radius of 1):

$$\sqrt{1/r}$$

So clearly you can see that you will go faster the closer you get to the event horizon.

You can always see how far you are from the singularity of a black hole by measuring your tidal acceleration, let's for instance consider you measure a tidal acceleration of 1g. Then you can calculate how much time you have to live till you reach the singularity (we again assume here you have a radial motion at escape velocity). Say you are 2 meters tall and experience a tidal effect of 1g, the time till ultimate doom for you becomes:

$${2 \over 3} \sqrt{{height \over acceleration}} = {2 \over 3} \sqrt{{2 \over 10}} = 0.2981423969$$

So about 0.3 seconds. If might be a consoling feeling that at least the duration of extreme discomfort is very short.

If you want to see how far you are from the event horizon in the above case you need to know how far the event horizon is from the singularity, if we make the event horizon rs =1 then we get:

$$(height / acceleration)^{1/3} = (2/10)^{1/3} = 0.5848035476$$

 

[DaveC426913]

I am not sure if it would be possible because maybe the black hole would evaporate before I would reach the event horizon,

- As the universe ages, the black hole evaporates faster. It has no mass to feed on, so it just continues to evaporate.

The EH deos not evaporate. I'm not sure how you concluded this.


It is more accurate to say nothing special happens as you pass it.

 

[kamenjar]

The EH deos not evaporate. I'm not sure how you concluded this.
It is more accurate to say nothing special happens as you pass it.

Hawking radiation?

 

[kamenjar]

The simplest term to use is to say that you want to pass the event horizon. The event horizon is a sphere and is two dimensional.

In my direction of travel it has only distance in the future, which is one dimension. It converges to me hitting it or not.

By the way, despite what many people think, it is not that easy to fall into a black hole, if you do not approach the black hole radially you have a good chance of passing it by.

I know. I meant direct dive.

As you approach it you would experience tidal effect but no time dilation.

I am point-like, so I have no tidal effects to experience.
OK, I would be subject to time dilation, though I would not experience it.

Sure your clock would be running slower if we compare it with some far away clock but for you that would not make any difference. Time would just go one second per second as always.

I think that I never said anything to the contrary. If I don't know formulas, doesn't mean that I can't visualize it.

It depends on how you travel, but if we assume radial motion at escape velocity your proper velocity going towards the event horizon will increase the closer you get to it.

Again, that also depends on how you travel, again if you travel radially at escape velocity you will see the restof the universe speed up but you will not, as many people seem to think, see the complete future of the history pass by when you reach the event horizon.

Why not? Well not complete history, but I can have a ratio of my second of my clock = 50 billion years of your clock, and that will just increase as I approach the event horizon anyways. Meaning that if it was to take 1 second for me to hit the event horizon, if the black hole will evaporate in 50 billion years, I will never hit it.

Don't you guys get what I am truing to say?

 

[kamenjar]

Yes, but it takes you a finite time to reach the event horizon by your own clock, and a finite time after that to reach the singularity.

If it was impossible for *you* to fall in before the black hole evaporated out from under you, then the same would be true for any particle accreting onto a non-accreting black hole.

What if the particles are stuck very near the event horizon and will continue on their (twisted by space-time) way past the event horizon once the hole evaporates or interact within the energy that it radiates and convert to different form?

Therefore it would be impossible for a black hole to form at all, because no particle could ever be the last particle to accrete.

I thought that these kinds of black holes form when the supermassive stars collapse on themselves. That stuff is in the singularity. I am removing accretion just because accretion causes event horizon to expand and maybe "swallow" matter into the singularity, so it would complicate the case.

So the question here isn't really whether it's impossible for you to fall into a black hole before it evaporates, it's whether it's impossible for a black hole to form in the first place, due to quantum effects.

They can form during he collapse or during accretion which gives significant mass and causes the event horizon to expand and "swallow" matter before it does evaporate. I assume that my small mass would not add to the total mass enough to swallow me before it evaporates.

That's a possibility that's been seriously proposed, but I don't think the mechanism is the one you're suggesting: http://arxiv.org/abs/0902.0346

Sry, I don't understand formulas.

I absolutely understand that you approach the black hole in finite time, but if time dilation (your clock vs rest-of-universe-clock) approaches infinite ratio, wouldn't that mean that in the last second of your trip, the universe will age billions of years (maybe not in last second, but very close), including that black hole?

Basically if I was to visualize my trip on a direct dive towards (absolute straight line path towards the ) the black hole, I would see universe around me start to age very fast... Planets and suns visibly moving.. Supernovas flashing like 4th of july, in last few moments Galaxy mergers etc etc.. Then the horizon escapes in front of me and dissipates as I zip by and continue on the same path, then "wake up" a few billion years after.

If I was super massive, I would see the event horizon expand faster because the enter of mass would tilt it towards me at a rate that is faster then evaporation.

My bests are placed on a fact that even though hawking radiation is small in Earth clock, it is quite significant in my time, especially in the last few moments before I reach the black hole. I am traveling at some finite (slow) speed, where particles that cause radiation are traveling at light speed and causing the radiation.

 

[George Jones]

Hawking radiation?

For more on what pervect posted, see near the bottom of

https://www.physicsforums.com/showthread.php?p=2899867&highlight=hawking#post2899867,

including the link at the very bottom to a diagram for an evaporating black hole.

 

[Passionflower]

Why not? Well not complete history, but I can have a ratio of my second of my clock = 50 billion years of your clock, and that will just increase as I approach the event horizon anyways. Meaning that if it was to take 1 second for me to hit the event horizon, if the black hole will evaporate in 50 billion years, I will never hit it.

Don't you guys get what I am truing to say?

I think I get what what you are trying to say, but I am not sure your are prepared to accept the answers I give. While it is true that you clock slows down more with respect to a far away clock going closer to the event horizon it is also true that the increase in velocity will redshift this result. The total effect will not be an infinite blueshift.

 

[kamenjar]

I think I get what what you are trying to say, but I am not sure your are prepared to accept the answers I give. While it is true that you clock slows down more with respect to a far away clock going closer to the event horizon it is also true that the increase in velocity will redshift this results. The total effect will not be an infinite blueshift.

I can tell you with 100% certainty that I was not prepared for this answer :)

Just messing around or are you saying that acceleration is also increasingly higher that I will fall into the black hole just because of that? I guess that's quite possible.

 

[DaveC426913]

What if the particles are stuck very near the event horizon and will continue on their (twisted by space-time) way past the event horizon once the hole evaporates or interact within the energy that it radiates and convert to different form?

I thought that these kinds of black holes form when the supermassive stars collapse on themselves. That stuff is in the singularity. I am removing accretion just because accretion causes event horizon to expand and maybe "swallow" matter into the singularity, so it would complicate the case.

They can form during he collapse or during accretion which gives significant mass and causes the event horizon to expand and "swallow" matter before it does evaporate. I assume that my small mass would not add to the total mass enough to swallow me before it evaporates.


Sry, I don't understand formulas.

I absolutely understand that you approach the black hole in finite time, but if time dilation (your clock vs rest-of-universe-clock) approaches infinite ratio, wouldn't that mean that in the last second of your trip, the universe will age billions of years (maybe not in last second, but very close), including that black hole?

Basically if I was to visualize my trip on a direct dive towards (absolute straight line path towards the ) the black hole, I would see universe around me start to age very fast... Planets and suns visibly moving.. Supernovas flashing like 4th of july, in last few moments Galaxy mergers etc etc.. Then the horizon escapes in front of me and dissipates as I zip by and continue on the same path, then "wake up" a few billion years after.

If I was super massive, I would see the event horizon expand faster because the enter of mass would tilt it towards me at a rate that is faster then evaporation.

My bests are placed on a fact that even though hawking radiation is small in Earth clock, it is quite significant in my time, especially in the last few moments before I reach the black hole. I am traveling at some finite (slow) speed, where particles that cause radiation are traveling at light speed and causing the radiation.

Point of order:

A dozen smartass responses are strangling each other in my mind in an all-out battle for control over my typing fingers. You have no idea how much self control I am exerting right now. And bcrowell might find himself having to do some explaining.



I'll just say that I am astonished at what does seem to be overlooked by PF's censor filter...


Keep reading...

Keeeeeeeep reading...

More...

Aaaaannnnd there you go.

 

[Passionflower]

I can tell you with 100% certainty that I was not prepared for this answer :)

Just messing around or are you saying that acceleration is also increasingly higher that I will fall into the black hole just because of that? I guess that's quite possible.

The inertial acceleration closer to the event horizon is definitely higher. For radial motion at escape velocity it is not much more complicated than for Newton. The inertial acceleration (remember you are free falling so there is no proper acceleration) is simply Newton divided by some factor dependent on the coordinate distance from the singularity, if we take a Schwarzschild radius of 1 we get:

$${'Newton' \over Some Factor} = {1 \over 2r^2}{1 \over \sqrt{1-1/r}}$$

Here is a graph showing your proper velocity and inertial acceleration going towards the event horizon:

As you can see both your proper velocity (which is the velocity as measured by a stationary observer when you pass by) and inertial acceleration increase going towards the event horizon. When you reach the event horizon your proper velocity is actualy c but, here is the catch, there cannot be a stationary observer at that location.

Since you are interested in the Doppler factor for a radially falling observer at escape velocity and an inertial observer at infinity I give you that formula as well (if I am not mistaken, which I sometimes are, others who know please verify it as well) and a chart so you can see what is happening as you cannot read formulas. If we take a Schwarzschild radius of 1 we get:

$${Gravitational Factor \over Velocity Factor} = \left( 1+\sqrt {{r}^{-1}} \right) ^{-1}$$

As you can see, the resulting Doppler factor actually decreases towards the event horizon.

Now how much is the Doppler factor exactly at the event horizon? Well in this case we have to take the limit of the above mentioned formula, which turns out in the case of rs=1 to be exactly 1/2. For any Schwarzschild radius this limit is:

$$\left( 1+\sqrt {{\it rs}} \right) ^{-1}$$

Where rs is the Schwarzschild radius.

By the way while it is false that 'the future of the universe will pass by' for a Schwarzschild solution it is actually true in case of a Kerr black hole, which is a rotating black hole, because it has a Cauchy horizon.

Aside:
Today my second son was born, on Schwarzschild's birthday (it's already 10/9 in China), his first name will be Nicolas but his middle name will be Karl.

 

[mrspeedybob]

If gravity and time dilation were infinite at the event horizon then what you say would be true and black holes could not form, but they are not infinite. They would be infinite dx from a singularity so you may never reach the center of the black hole, but time would pass at a finite rate as you cross the event horizon.

 

[JesseM]

If gravity and time dilation were infinite at the event horizon then what you say would be true and black holes could not form, but they are not infinite. They would be infinite dx from a singularity so you may never reach the center of the black hole, but time would pass at a finite rate as you cross the event horizon.

"Time dilation" can really only be defined relative to a choice of coordinate space--it's a measure of how slow a physical clock ticks compared to coordinate time. In Schwarzschild coordinates the number of clock ticks per second of coordinate time actually does approach zero as a clock approaches the horizon, but this is just a consequence of how the Schwarzschild coordinate system is defined, other coordinate systems in the same black hole spacetime (various ones are listed on the bottom half of this page) don't have the property that the time dilation goes to infinity on the horizon.

 

[stevebd1]

I am not sure if it would be possible because maybe the black hole would evaporate before I would reach the event horizon,

http://cfpa.berkeley.edu/Education/BHfaq.html#q9"

http://antwrp.gsfc.nasa.gov/htmltest/gifcity/bh_pub_faq.html#evaporate"

 

[kamenjar]

http://cfpa.berkeley.edu/Education/BHfaq.html#q9"

http://antwrp.gsfc.nasa.gov/htmltest/gifcity/bh_pub_faq.html#evaporate"

I was actually reading those articles before I posted, but none explained the reasoning why this is the case. Basically it says that you do fall into the black hole. That's it.

Hawking radiation was discovered after Einstein died. Einstein thought that black holes live forever and that's why he thought that there was a singularity and that matter falls into the black hole singularity.

The claim is that there is no singularity and that the spacetime is just severely warped around the black hole and that matter is accumulated at the crust and "trapped in time" from our viewpoint. That trapped matter is waiting to be converted into energy or continue to exist once the black hole evaporates, depending on when it entered the gravitational field.

Come to think of it more, even feeding of the black hole does not affect this. Just more and more matter/mass gets trapped into the spacetime when the black hole is "fed" and nothing crosses the Schwarzschild radus.

I'm definitely not claiming that what I'm saying is true. But other than derived math, I've not yet seen any convincing answer.

 

[DaveC426913]

Come to think of it more, even feeding of the black hole does not affect this. Just more and more matter/mass gets trapped into the spacetime when the black hole is "fed" and nothing crosses the Schwarzschild radus.

Everything does cross the EH, it is only the distortion of light signature that makes it look that way, and only from an external frame of reference. Don't confuse the two.

For example, note that gravitational effects due to infalling mass are not affected by the EH.

 

[Passionflower]

But other than derived math, I've not yet seen any convincing answer.

If the math does not convince you what will?

You seem to have made a conclusion, I am afraid that no one will be able to convince you that you are wrong. So I am not sure why you keep asking questions if you have already made up your mind about things, the answers will not change in time.

 

[kamenjar]

Well thanks for all your replies. I'm going to do some reading and hopefully this clears up.

In the meanwhile, since you guys like formulas, maybe someone would be in a mood to answer this:
If black hole had was one solar mass in size, and I was at rest 1AU from the center of it, how much would the universe "age" by the time I fall into the black hole?

 

[Passionflower]

Here is a picture from the perspective of a static observer seeing things fall towards the black hole.

Taken from Susskind, Lindesay - "An Introduction to Black Holes Information and the String Theory Revolution"

 

[Dale]

But other than derived math, I've not yet seen any convincing answer.

Then you should go learn the math. Your question has been answered.

To add my 2 cents:

1) If you are falling into a black hole then it is accreting by definition. The impossibility of falling into a non-accreting black hole is an inapplicable tautology.

2) Don't forget the cosmic background radiation. Only very small black holes can evaporate, the rest are colder than the CMBR and therefore radiate less energy than they receive.

 

[JesseM]

In the meanwhile, since you guys like formulas, maybe someone would be in a mood to answer this:
If black hole had was one solar mass in size, and I was at rest 1AU from the center of it, how much would the universe "age" by the time I fall into the black hole?

Are you asking what would be seen visually? Like if you could see a clock very far from the black hole and you saw it reading 2000 AD at the moment you started falling from 1 AU, what time would you see on that clock as you were crossing the event horizon? Or are you asking how much coordinate time would elapse between beginning to fall and crossing the horizon in some particular coordinate system? (it would be infinite if we were talking about Schwarzschild coordinate time, but finite in some other coordinate systems like the ones listed on the bottom half of this page)

 

[Passionflower]

In the meanwhile, since you guys like formulas, maybe someone would be in a mood to answer this:
If black hole had was one solar mass in size, and I was at rest 1AU from the center of it, how much would the universe "age" by the time I fall into the black hole?

What would be the point? I already showed you that calculating the Doppler shift for a free falling object at escape velocity does not give an infinite blue shift at the EH. That apparently did not convince you, so why would this calculation make any difference? I would predict your answer to be something like "well yes the math shows it but I am still not convinced".

And yes, if you want to do science, you have to like formulas, without using formulas it is simply guess work.

 

[DaveC426913]

Are you asking what would be seen visually? Like if you could see a clock very far from the black hole and you saw it reading 2000 AD at the moment you started falling from 1 AU, what time would you see on that clock as you were crossing the event horizon?

That does seem to be what he's asking. How much would the universe age?

 

[kamenjar]

That does seem to be what he's asking. How much would the universe age?

Right. And calculations I've seen are only for proper time. I was hoping that something interesting would pop up like - is the black hole actually there once you reach it because so much of the universe's time as passed. I figure that when you look at the black hole, you are looking at WAS, but maybe not IS in your proper time. Gravity also propagates at speed of light, so there's no saying that in your proper time there IS a black hole. There's maybe threshold between IS and WAS.

I was also reading on Mach's principle, so I think that it also implies that there is no singularity because there's no matter on the other side and you can't fall towards it, though I am not certain about this.

I've also seen dilation calculation. TBH, I don't understand them. I'm a programmer, not a physicist, so I apologize in advance if my level of understanding is just not sufficient. I would be happy to do a simulation on this, if I had the input.

 

[DaveC426913]

is the black hole actually there once you reach it because so much of the universe's time as passed. I figure that when you look at the black hole, you are looking at WAS, but maybe not IS in your proper time.

Still not sure how you arrive at this. You are falling into the BH; unlike the rest of the universe, the BH is not aging before your eyes.

Gravity also propagates at speed of light, so there's no saying that in your proper time there IS a black hole. There's maybe threshold between IS and WAS.

Slight correction. Gravity is a field, so it was there from the beginning (which is why we don;t worry about "how gravity can escape from a BH"). It is only changes to gravity that propagate at the speed of light.

 

[Passionflower]

I've also seen dilation calculation. TBH, I don't understand them. I'm a programmer, not a physicist, so I apologize in advance if my level of understanding is just not sufficient. I would be happy to do a simulation on this, if I had the input.

You can read a graph right? Did you actually look at the graph? Did you see that the gravitational and velocity based time dilation work against each other?

 

[kamenjar]

Still not sure how you arrive at this. You are falling into the BH; unlike the rest of the universe, the BH is not aging before your eyes.

Hmm I am not sure why you think that.

Here is an example... Star X, at t=0 20 light years away from earth. Earth "sees" that in 20 years we would see the star explode into a supernova. And let's say that in 20 years we do see it explode.
Now if 20 years before we could see the explosion, if I was a suicide tourist that wanted to see this for myself and die, and was to take off from Earth towards Star X that is 20 light years away, it could maybe only take me a few years of proper time to get there, but I would still take 20 Earth years to get there, and the star would go supernova before I got there. (In fact, it already DID). I can not travel faster than light, nor can events. So that star only WAS and no longer IS in my time arrow. I was too late. It's a proof that star is no longer there in my timeframe. I could've never reached it before it blew up, no matter how fast I flew, no matter how much I accelerated (black hole or whatnot) and how long of my proper time it took to get there. Unless I took off from from something that was closer or earlier in time. So there was a "threshold" of me reaching the star before it went supernova and that threshold only depended on me being within 20 LY away from it and that threshold only kept getting closer to the star as time passed by and distance increased. You can think of it as an "supernova event horizon" = you are within it, you can suicide with supernova.

Now a mathematician will say "well we'll just PLACE you 19 LY away, and there, the formula proves that you can reach the supernova". Well that the does THAT mean? Do you mean teleport me or or move me from Earth to that place in speed of light? In the former case, I never said that the star was there 1 year ago. I only said that we saw the star at t=0. In the second case, nothing changed. We never saw a black hole form, and we know very little about that so we can't just teleport near it to see it form and/or fall into it. We have to take it from t=0, and at t=0, the closest black hole is maybe 3000LY away.

I only see the light and gravity from the black hole's object near EH long time ago. My thought process is based on this - Due to the high gravity redshift and time dilation of objects very near to EH, the black hole EH "behaves" similarly to a distant object in space and in time. What is worse, I think that it even behaves as an infinitely distant object unless it changes mass and evaporates. Similarly to the above example, it may take me 0.2 seconds to reach the EH, but did I reach an EH or an aged black hole that evaporated AKA=reached nothing?

Slight correction. Gravity is a field, so it was there from the beginning (which is why we don;t worry about "how gravity can escape from a BH"). It is only changes to gravity that propagate at the speed of light.

Right but the WAS field. Not IS, or reachable field. the gravity will also change assuming Hawking radiation theory is true. We will not see this gravity change yet.

Edit: rephrased and clarified.

 

[kamenjar]

You can read a graph right? Did you actually look at the graph? Did you see that the gravitational and velocity based time dilation work against each other?

I did, but I don't comprehend time dilation decreasing. I thought you increase proper speed towards something, time dilation always increases.

You also talk about EH radius... How do you measure a radius of a black hole? How big is something in an infinitely stretched space? How can you even measure it. And how do you measure distance from singularity which is not even there to begin with - there is no matter in direction of measurement, there is no time nor speed of light to measure by. It is all just much harder for me to comprehend something if I involve those terms.

And in addition, read my above example and understand that I can't take just some distances as examples. How do you even measure distance from EH? EH is infinitely far away in my head because objects are infinitely red shifted and so faint that we can't see them with best telescopes. If you were not to see the lensing effect, how would you see the difference between something that was billions of years away and something that is near the black hole EH? So you can't just throw some formula and calculate something and assume that EH is there even to begin with. We see distant objects, but by the time we get to them, they may not be even there. That's why I resort to logic and not just bare formulas because by logic you have to establish a state for the formula.

I really appreciate your attempts to teach me, but I can't understand the basic concepts that you take from granted because you know them, and you draw conclusions based on them. I have to understand those concepts before I can draw the conclusions the same way you do.