Value of g near a black hole (re-visited)

[pawprint]

I've engaged with several threads concerning simple (i.e. non-rotating, uncharged) black holes. My general line of argument has been that, as apparent time becomes infinitely stretched at the event horizon nothing can be observed to enter the BH in finite time. jambaugh wrote two lengthy dissertations on this at the end of the thread "Can a black hole suck in another black hole?"

I even began a thread- "Value of g near a black hole" directly asking for confirmation. It read- "On approach to a simple (non-rotating, uncharged) singularity, does g increase asymptotically near...
a) the singularity,
b) its event horizon,
or c) no?"
...to which I understood the answers to point towards b).

Nobody has disputed these assertions, unless it was in mathematics beyond my understanding. Now please let's keep this thread related only to 'simple' BHs.

I now believe my prior understanding (which is intuitive rather than mathematical) was flawed. I propose that gravity approaches infinity asymptotically at the singularity, not the EH. The EH of a simple BH can surely be defined as the distance from the singularity at which escape velocity = c.

Can a purely Newtonian approach be used for calculations at discernable distances from the singularity?

Comments please :{)

 

[PeterDonis]

I even began a thread- "Value of g near a black hole"

I assume the previous thread you are referring to is this one?

https://www.physicsforums.com/showthread.php?t=576973

If so, yes, the answer you were given is b), and it is the correct answer.

I now believe my prior understanding (which is intuitive rather than mathematical) was flawed. I propose that gravity approaches infinity asymptotically at the singularity, not the EH.

Why do you think the answer you were given in the previous thread is wrong? If it's because of this...

Can a purely Newtonian approach be used for calculations at discernable distances from the singularity?

...then it's not a valid reason, because the answer to the question just quoted is "no". A "purely Newtonian" approach will give incorrect answers unless you are at a radial coordinate r that is much, much larger than the Schwarzschild radius (2M), so that the error in the Newtonian formulas becomes too small to measure.

 

[pawprint]

Yes, that is the thread referred to. Sorry I did not know how to find it as showthread.php?t=576973.
I would prefer to wait before addressing questions raised, as they are likely to come in bunches. However I certainly wouldn't apply Newton to orbits. Only F=(m1*m2)/D².

 

[PeterDonis]

Sorry I did not know how to find it as showthread.php?t=576973.

If you're trying to find a thread you have participated in, the easiest way I know of is to click on "My PF", and then click on the "List Subscriptions" link on the left of the screen. That will show you a list of all the threads you have posted in, in reverse chronological order (most recent at the top).

 

[pervect]

If you take the time to look this up in some GR textbooks, or some of the GR Faq's, you should be easily able to find out that objects can fall past the event horizon in finite proper time.

Depending on your background (I don't know what it is) you may or may not be able to follow the calculations yourself, but you should be able to find the answer written down in a number of places.

FOr instance the sci.physics.faq: http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

Won't it take forever for you to fall in? Won't it take forever for the black hole to even form?

Not in any useful sense. The time I experience before I hit the event horizon, and even until I hit the singularity—the "proper time" calculated by using Schwarzschild's metric on my worldline—is finite. The same goes for the collapsing star; if I somehow stood on the surface of the star as it became a black hole, I would experience the star's demise in a finite time.

 

[bcrowell]

a) the singularity,
b) its event horizon,
or c) no?"
...to which I understood the answers to point towards b).

Nobody has disputed these assertions, unless it was in mathematics beyond my understanding.

I disputed it. As I explained in the previous thread, g has any value you like, depending on your coordinates.

If so, yes, the answer you were given is b), and it is the correct answer.

No, it's not correct without some further qualification, such as specifying coordinates or a frame of reference.

What the OP needs to understand at this point, and doesn't seem to, is that this becomes a crucial point inside the horizon, where there are no stationary observers.

 

[Nabeshin]

I've engaged with several threads concerning simple (i.e. non-rotating, uncharged) black holes. My general line of argument has been that, as apparent time becomes infinitely stretched at the event horizon nothing can be observed to enter the BH in finite time. jambaugh wrote two lengthy dissertations on this at the end of the thread "Can a black hole suck in another black hole?"

I even began a thread- "Value of g near a black hole" directly asking for confirmation. It read- "On approach to a simple (non-rotating, uncharged) singularity, does g increase asymptotically near...
a) the singularity,
b) its event horizon,
or c) no?"
...to which I understood the answers to point towards b).

Nobody has disputed these assertions, unless it was in mathematics beyond my understanding. Now please let's keep this thread related only to 'simple' BHs.

I now believe my prior understanding (which is intuitive rather than mathematical) was flawed. I propose that gravity approaches infinity asymptotically at the singularity, not the EH. The EH of a simple BH can surely be defined as the distance from the singularity at which escape velocity = c.

Can a purely Newtonian approach be used for calculations at discernable distances from the singularity?

Comments please :{)

Again, I think my post in your previous thread perfectly describes the situation. But it does have qualifications and you have to read it carefully! I am not knitpicking!

Furthermore, when you say 'gravity' goes to infinity, you need to be specific in what you mean. Most (relativists) would take this to mean the invariant curvature goes to infinity, which is indeed true at the singularity (so this is not a coordinate effect). However, nothing haywire takes place with the curvature at the event horizon.

Just a general note about applying Newtonian reasoning to objects like black holes... although it gives some correct answers (i.e. schwarzschild radius), it doesn't make much sense. For example, in the Newtonian picture, a light ray shot away from the event horizon will continue along OUT TO INFINITY. This is of course absurd, you can't communicate from beyond the event horizon! A truer picture would be, you shoot a light ray 'radially outward' but in fact the light cones are so tipped that this direction corresponds to the interior of the black hole. My point is, unfortunately, you cannot apply Newtonian reasoning and trying to use Newtonian intuition is likely to lead you to wrong conclusions. (Edit: This is actually the apparent horizon I am describing, which corresponds to the event horizon in the case of a stationary spacetime)

 

[pawprint]

I have read all responses and suggested references. I don't want to change the original question but merely re-frame it.

1) The EH is at a radius from the singularity where escape velocity on the inner side is greater than c, and on the outer side is less than c. Correct?

2) How can a 'non-infinite' escape velocity be reconciled with a practically infinite value of gravity at the same radius? This is what you appear to be asserting.

If the answers require great mathematical insight then I withdraw. Surely they can be expressed more simply.

 

[PAllen]

I have read all responses and suggested references. I don't want to change the original question but merely re-frame it.

1) The EH is at a radius from the singularity where escape velocity on the inner side is greater than c, and on the outer side is less than c. Correct?

2) How can a 'non-infinite' escape velocity be reconciled with a practically infinite value of gravity at the same radius? This is what you appear to be asserting.

If the answers require great mathematical insight then I withdraw. Surely they can be expressed more simply.

As several people have already said, everything depends on what you mean by gravity, especially as you are thinking by analogy to Newtonian gravity.

One concept of gravity is called 'tidal gravity': even if a moon is in free fall or orbiting a massive body, different parts of it are pulled in different directions so it is under stress: tidal stress. This is the sense of gravity that, in GR, corresponds to curvature and is not a coordinate dependent feature. It is the feature that causes a star approaching a small black hole to be torn apart. Here, I mean small in size compared to a star, but with mass of several stars. And by size, I mean the event horizon. This sense of gravity only becomes infinite on approach to the singularity itself. For a super-massive black hole (a billion suns, for example), tidal gravity at the horizon is quite small.

A different concept of gravity is what you think of as how hard you are pulled to the ground, which is better viewed as how hard the ground is pushing to keep you from moving on a free fall path. For a simple, static black hole, the notion of static observer is well defined outside the event horizon, while being impossible on or inside the event horizon. For a static observer very slowly approaching an event horizon, the thrust needed to hold a static position goes to infinity as you approach the horizon. Note that the velocity needed relative to a static observer required to escape to infinity approaches c as a static observer approaches the event horizon.

 

[pawprint]

Thank you PAllen. I understand both concepts and have no difficulty with their differences. I would not presume to post on PhysicsForums otherwise.

The nub of my question, however, may point to a lack of understanding. A clock on a floor on Earth runs a little slower (about 1 part in 10¹⁷ I think) than one on a metre-high table.

I would expect a clock near a singularity to run near infinitely slowly regardless of observation. Yet 'common knowledge', (including many posts in PF), says that this occurs at the event horizon of a black hole, where, as you point out, the gravitational gradient may be quite low.

I don't see why, in this instance, 'tidal gravity' should behave differently, because it is the same (Einsteinian) sort of gravity which is responsible for the Earth-bound clocks' disagreements. What am I missing?

 

[Nabeshin]

Thank you PAllen. I understand both concepts and have no difficulty with their differences. I would not presume to post on PhysicsForums otherwise.

The nub of my question, however, may point to a lack of understanding. A clock on a floor on Earth runs a little slower (about 1 part in 10¹⁷ I think) than one on a metre-high table.

I would expect a clock near a singularity to run near infinitely slowly regardless of observation. Yet 'common knowledge', (including many posts in PF), says that this occurs at the event horizon of a black hole, where, as you point out, the gravitational gradient may be quite low.

I don't see why, in this instance, 'tidal gravity' should behave differently, because it is the same (Einsteinian) sort of gravity which is responsible for the Earth-bound clocks' disagreements. What am I missing?

You have to compare two clocks to do what you are talking about. I can compare my clock to a clock a meter higher, or a far away observer can compare his clock to that of his buddy, who is hovering just outside the event horizon. Once you put the clock past the event horizon, it is no longer possible to compare it to the outside clock! The two are causally disconnected! Keep in mind, that if YOU were the one falling into a black hole (and you've got really stiff bones, so you don't get ripped apart easily) watching your own clock, you would see nothing strange at all as you approached the singularity. Time will tick by always at the rate of 1 second per second.

 

[pawprint]

*This has crossed over Nabeshin's last post.*

Eureka!

I think I have it. The clock does not slow except as expected. It is only the outside observer who sees it do so, and that is not a phenomenon of gravity, but of light.

Do I win my own prize? If so I wouldn't have realized this without your help.

 

[pawprint]

Clarification: "The clock does not slow except as expected." means as expected by Einsteinian gravity.

If this is correct then my question (previous post noted in first post of this thread) should be answered a) not b). It only LOOKS like b).

 

[PeterDonis]

No, it's not correct without some further qualification, such as specifying coordinates or a frame of reference.

You're right, I should have qualified my answer by saying that b) is the answer if "g" means "the proper acceleration of an observer who is at a constant radial coordinate r for all time". From reading the previous thread it appeared that that was the definition of "g" that had been settled on.

What the OP needs to understand at this point, and doesn't seem to, is that this becomes a crucial point inside the horizon, where there are no stationary observers.

Good point; that's often a stumbling block.

 

[questionpost]

How come I don't get the feeling of infinitely stretch space time from a finitely deep gravitational well who's escape velocity just coincidentally happens to exceed light at some random value? We don't even know if there actually is a fabric of space, it's just a mathematical representation of how gravitational fields change over distance.

 

[pervect]

Thank you PAllen. I understand both concepts and have no difficulty with their differences. I would not presume to post on PhysicsForums otherwise.

The nub of my question, however, may point to a lack of understanding. A clock on a floor on Earth runs a little slower (about 1 part in 10¹⁷ I think) than one on a metre-high table.

I would expect a clock near a singularity to run near infinitely slowly regardless of observation. Yet 'common knowledge', (including many posts in PF), says that this occurs at the event horizon of a black hole, where, as you point out, the gravitational gradient may be quite low.

I don't see why, in this instance, 'tidal gravity' should behave differently, because it is the same (Einsteinian) sort of gravity which is responsible for the Earth-bound clocks' disagreements. What am I missing?

A stationary clock near a singularity would run slow when compared with another stationary clock that's far away from any singularity, and it'd approach stopping as the stationary clock got closer and closer to the event horizon.

There's no such thing as a stationary clock at the event horizon, however. In fact, any clock crossing the event horizon must be moving at the speed of light - or rather, since the event horizon can be thought of as trapped light, any physical infalling clock, which is stationary in its own frame, will see the event horizon approaching it at the speed of light.

This motion causes signficant SR effects. If you neglect the velocity effects, it would be correct to say that from the point of view of an infalling observer, a clock at infinity would run faster and faster, without bound, as one approached the event horizon,.

When you include the velocity effects, though, the clock at infinity doesn't run infinitely fast.

You will run into the usual special relativity (SR) issues associated with the twin paradox when you include the velocity effects - I'm not sure what yoru background is in SR.

 

[questionpost]

Why are people making all this hype about the event horizon? That's just an escape velocity boundary, what we should really worry about a singularity. Also, I thought it was impossible for matter to travel at the speed of light, I even had a separate topic just for that and someone posted a Lawrence transformation.

 

[pervect]

Why are people making all this hype about the event horizon? That's just an escape velocity boundary, what we should really worry about a singularity.
Also, I thought it was impossible for matter to travel at the speed of light, I even had a separate topic just for that and someone posted a Lawrence transformation.

It is impossible for matter to travel at the speed of light. You say that as if someone said otherwise??

 

[Naty1]

Why are people making all this hype about the event horizon?

Can you explain what you think is 'hype'?

The horizon is a very interesting boundary...and if fully understood might reveal some underlying relationships difficult or impossible to otherwise detect. Not so long ago, black holes and horizons here virtually 'science fiction'...Einstein, for eample, did not initially believe they could exist.

Here are two descriptions that reveal some of that 'character' of horizons:


Kip Thorne says (Lecture in 1993 Warping Spacetime, at Stephan Hawking's 60th birthday celebration, Cambridge, England,)

The flow of time slows to a crawl near the horizon, and beneath the horizon time becomes so highly warped that it flows in a direction you would have thought was spacial: it flows downward towards the singularity. That downward flow, in fact, is why nothing can escape from a black hole. Everything is always drawn inexorably towards the future, and since the future inside a black hole is downward, away from the horizon, nothing can escape back upward, through the horizon.

and this one from Mitchell Porter [ a forum paritcipant]:

... the idea is that the interior of the black hole has a dual (holographic) description in terms of states on the horizon; a lot like AdS/CFT, with the horizon being the boundary to the interior. So when someone crosses the horizon from outside, there's a description which involves them continuing to fall inwards, until they are torn apart by tidal forces and their degrees of freedom redistributed among the black hole's degrees of freedom, all of which will later leak away via Hawking radiation; but there's another description in which, when you arrive at the horizon, your degrees of freedom get holographically smeared across it, once again mingling with all the black hole's prior degrees of freedom (also located on the horizon), which all eventually leak away as Hawking radiation

 

[questionpost]

Can you explain what you think is 'hype'?

The horizon is a very interesting boundary...and if fully understood might reveal some underlying relationships difficult or impossible to otherwise detect. Not so long ago, black holes and horizons here virtually 'science fiction'...Einstein, for eample, did not initially believe they could exist.

Here are two descriptions that reveal some of that 'character' of horizons: Kip Thorne says (Lecture in 1993 Warping Spacetime, at Stephan Hawking's 60th birthday celebration, Cambridge, England,)



and this one from Mitchell Porter [ a forum paritcipant]:

How come I don't see this "infinite warping and time flowing backwards" when I look at a computer model that just shows a finitely deep well? It doesn't even make sense that time would stop, because then how would anything ever reach the singularity to add to its mass?

 

[pervect]

How come I don't see this "infinite warping and time flowing backwards" when I look at a computer model that just shows a finitely deep well? It doesn't even make sense that time would stop, because then how would anything ever reach the singularity to add to its mass?

Time isn't absolute. If you'll recall from special relativity (and if you don't recall it from special relativity, it's really helpful to learn some before trying to tackle General Relativity), it's possible for someone in frame A to conclude that frame B's clock's run slow, while someone in frame B concludes that A's clocks run slow. This is a consequence of the relativity of simultaneity.

It may also be helpful to note that event horizons, very much like the event horizons of a black hole, form in special relativity whenever an observer accelerates - the so called Rindler horizion. A consideration of the Rindler horizon can be very helpful in understanding the event horizon of a black hole.

There's some discussion of this at http://www.gregegan.net/SCIENCE/Rindler/RindlerHorizon.html, using basic calculus (no tensors).

The quick explanation is that a clock stopping is not an absolute fact, but some observers might see a clock as stopped, and other observers won't.

 

[questionpost]

Yeah, some people "would" see time as being stopped *If it was possible* to do things like travel at the speed of light or infinitely warp the fabric of space. The event horizon for a black hole seems like just an extension of Rindler logic, but as with other examples in relativity such as with relative velocity, you can't use the "Va +Vb= total velocity" for two objects moving away from each other near the speed of light, you need a completely different and more accurate equation that asymtotes at c which is specifically helpful for extremes such as when you have two objects approaching the speed of light.
However, I have yet to see any experiment where we actually see the clocks completely stopped or moving backwards as a result of the somehow infinite distortion of the fabric of space. The event horizon isn't even a physical boundary, it's just the given distance from the singularity at which you can't escape unless you accelerate faster than light. There's still infinitessimal amounts of escape velocities higher than the speed of light inside the event horizon, and there's an infinitessemal escape velocities less than the speed of light outside of it, for some reason people just happen to focus on the escape velocity that is exactly c.
This reminds me of when people said time traveling to the past or distant future was possible just because they saw electrons jumping from one point to another without appearing in the intervening space, and it turns out it had nothing to do with the speed of light or even time, it's completely different math and completely different things that are happening.

 

[PAllen]

I dispute the meaning of "escape velocity" inside the horizon. For one thing, you have to be able to escape for this to have meaning. Any tiny region inside the horizon looks just like a tiny region of interstellar space. Matter can only only travel on timelike paths, light on null paths, thus there is no escape path at all, period.

Another way of looking at this is that escape velocity is outside the horizon is defined relative to static observers (you can never talk about any velocity without specifying what it is relative to). Well, there are no static observers at or inside the horizon.

So forget this nonsense about 'escape velocity' greater than c.

 

[questionpost]

I dispute the meaning of "escape velocity" inside the horizon. For one thing, you have to be able to escape for this to have meaning. Any tiny region inside the horizon looks just like a tiny region of interstellar space. Matter can only only travel on timelike paths, light on null paths, thus there is no escape path at all, period.

Another way of looking at this is that escape velocity is outside the horizon is defined relative to static observers (you can never talk about any velocity without specifying what it is relative to). Well, there are no static observers at or inside the horizon.

So forget this nonsense about 'escape velocity' greater than c.

Well there's the problem right there, because contrary to what your saying what reality is, which is based on improper extrapolations of math in the same way as how I was saying, I can punch in an equation for escape velocity based on gravity and find it eventually gets to a point where it's larger than light. Even if it's physically impossible to have that relative point, I can use my calculator and still find a greater escape velocity than light the same way that you can punch in an equation and calculate that the fabric of space is "infinitely" warped or that time moves backwards.

 

[PAllen]

However, I have yet to see any experiment where we actually see the clocks completely stopped or moving backwards as a result of the somehow infinite distortion of the fabric of space.

You will never see an experiment showing clocks moving backwards if GR is true because there is no such prediction in GR (even on a closed time like curve you don't see a clock moving backwards). As for completely stopped, you only see this as limiting condition whether you are watching a black hole from a distance or watching ever more accelerated particles. We certainly see particles whose decay clocks are slowed by a factor a millions or more. Damn close to being stopped.

 

[PAllen]

Well there's the problem right there, because contrary to what your saying what reality is, which is based on improper extrapolations of math in the same way as how I was saying, I can punch in an equation for escape velocity greater than gravity and find it eventually gets to a point where it's larger than light. Even if it's physically impossible to have a relative point, I can use my calculator and still find a greater escape velocity the same way that you can punch in an equation and calculate that the fabric of space is "infinitely" warped or that time moves backwards.

We're discussing GR in this forum. If you want to discuss some other theory, go somewhere else. If you think GR predicts 'greater than c' escape velocity, you better explain what you mean in GR terms. You would be wrong, but we can discuss misunderstandings of GR here.

 

[questionpost]

We're discussing GR in this forum. If you want to discuss some other theory, go somewhere else. If you think GR predicts 'greater than c' escape velocity, you better explain what you mean in GR terms. You would be wrong, but we can discuss misunderstandings of GR here.

GR says as you distort the fabric of space more, the slower time moves in that distortion relative to an outside observer right? Well if we can't have an outside observer, how do we actually know that what your saying is true about the fabric of space with a black hole especially if I can use an equation to "prove" the existence of greater escape velocities than light?
If time wasn't flowing relative to an observer inside the black hole, then the couldn't possibly see that the singularity is coming closer to them because they couldn't be traveling distance over time since for them time has stopped right? So they would never reach the singularity, according to the math alone...
They would have to travel distance over time in order to reach the singularity, because the singularity is x distance away from the observer, unless the event horizon somehow is the singularity. I can even read books that say something like "oh yeah, it would take a week or so for an in-falling person to reach the very center of a massive black hole".
It doesn't even make sense when people say "We would see that light get's frozen at the event horizon" because we wouldn't ever be able to observe if the photons are trapped at the event horizon because then they wouldn't be able to make it to our eyes if they were frozen.

 

[PAllen]

GR says as you distort the fabric of space more, the slower time moves in that distortion relative to an outside observer right? Well if we can't have an outside observer, how do we actually know that what your saying is true about the fabric of space with a black hole especially if I can use an equation to "prove" the existence of greater escape velocities than light?
If time wasn't flowing relative to an observer inside the black hole, then the couldn't possibly see that the singularity is coming closer to them because they couldn't be traveling distance over time right? So they would never reach the singularity, according to the math alone...

I'm not saying we can know or observe what happens inside an event horizon. Therefore, it is meaningless to discuss what 'really' happens inside, and is outside the scope of this forum. However, we can discuss what GR, as a theory, predicts happens inside, for different types of black holes.

GR predicts time flow perfectly normally for an observer crossing the horizon, and allow calculation of exactly how much time (quite short) before they reach the singularity. An outside observer sees them slow down, darken, and fairly quickly become invisible.

I repeat, if you want to talk about something other than GR, you need to do that in a different forum. If you dispute what GR predicts, please explain where everyone else is mis-interpreting the math of GR.

 

[questionpost]

I'm not saying we can know or observe what happens inside an event horizon. Therefore, it is meaningless to discuss what 'really' happens inside, and is outside the scope of this forum. However, we can discuss what GR, as a theory, predicts happens inside, for different types of black holes.

GR predicts time flow perfectly normally for an observer crossing the horizon, and allow calculation of exactly how much time (quite short) before they reach the singularity. An outside observer sees them slow down, darken, and fairly quickly become invisible.

I repeat, if you want to talk about something other than GR, you need to do that in a different forum. If you dispute what GR predicts, please explain where everyone else is mis-interpreting the math of GR.

Some of what was said GR predicts doesn't seem to coincide with what other aspects predict...
How does time flow so perfectly normal if the fabric of space is "infinitely" warped and matter would follow that warp or if time flows backwards or "downwards"? If time went the other way, wouldn't you travel further away from the singularity since matter will follow the path of the fabric of space-time only to perpetually approach the event horizon to try and cross into the rest of the universe and thus not make it to the singularity? Or might you even be "stuck" at the event horizon because time flowing the other way would mean your exiting the black hole yet outside the black hole time is flowing forwards?
There should just be a few weird things that might happen, but instead there's all sorts of different things that contradict themselves.
I mean, we can predict what would happen if matter went at the speed of light yet have an equation right next to it that says matter cannot travel at the speed of light because it's speed asymtotes at C.

 

[PAllen]

Some of what was said GR predicts doesn't seem to coincide with what other aspects predict...
How does time flow so perfectly normal if the fabric of space is "infinitely" warped of if time flows backwards or "downwards"? If time went the other way, wouldn't you travel further away from the singularity since matter will follow the path of the fabric of space-time only to perpetually approach the event horizon to try and cross into the rest of the universe and thus not make it to the singularity?

Warped is a poetic term, not physics or mathematics. The accurate statement is: there is a curvature singularity inside a black hole horizon. There is no singular or extreme local behavior at the horizon of a sufficiently large black hole. Time flowing backwards or downwards is simply nonsense, not part of GR at all. Where are you getting this from? Probably you are reading nonsense and believing it is an accurate portrayal of GR.

 

[questionpost]

Warped is a poetic term, not physics or mathematics. The accurate statement is: there is a curvature singularity inside a black hole horizon. There is no singular or extreme local behavior at the horizon of a sufficiently large black hole. Time flowing backwards or downwards is simply nonsense, not part of GR at all. Where are you getting this from? Probably you are reading nonsense and believing it is an accurate portrayal of GR.

Not to single them out, but stuff like this as well as the books of people like Michio Kaku and Brian Green are confusing or conflicting.

and it'd approach stopping as the stationary clock got closer and closer to the event horizon.

There's no such thing as a stationary clock at the event horizon,

since the event horizon can be thought of as trapped light, any physical infalling clock, which is stationary in its own frame, will see the event horizon approaching it at the speed of light.

Can you explain what you think is 'hype'?
Here are two descriptions that reveal some of that 'character' of horizons: Kip Thorne says (Lecture in 1993 Warping Spacetime, at Stephan Hawking's 60th birthday celebration, Cambridge, England,)
The flow of time slows to a crawl near the horizon, and beneath the horizon time becomes so highly warped that it flows in a direction you would have thought was spacial: it flows downward towards the singularity. That downward flow, in fact, is why nothing can escape from a black hole. Everything is always drawn inexorably towards the future, and since the future inside a black hole is downward, away from the horizon, nothing can escape back upward, through the horizon.

I get that time slows relative to an observer as distortion increases, but just as with traveling at the speed of light, it seems like that should only happen asymtotically. Stopping? From an outside observer's calculations, the in-falling object should never reach the singularity and thus the black hole would never gain mass relative to the outside observer even though the in-falling object would hit the singularity and add to it's mass? And time flowing towards the future infinitely or what?
The gravitational or electric field of a black hole is suppose to be time-frame independent, so how would you measure a change in it originating from the singularity once mass added to it especially if you can't even observer an object crossing the event horizon?

 

[Nabeshin]

I get that time slows relative to an observer as distortion increases, but just as with traveling at the speed of light, it seems like that should only happen asymtotically. Stopping? From an outside observer's calculations, the in-falling object should never reach the singularity

Correct. More specifically, the observer will never be seen to cross the event horizon.

and thus the black hole would never gain mass relative to the outside observer even though the in-falling object would hit the singularity and add to it's mass?

False, see my post here: https://www.physicsforums.com/showpost.php?p=3771662&postcount=10

 

[PeterDonis]

From an outside observer's calculations, the in-falling object should never reach the singularity and thus the black hole would never gain mass relative to the outside observer even though the in-falling object would hit the singularity and add to it's mass?

The infalling object doesn't have to reach the singularity to increase the black hole's mass. Actually, it doesn't even have to reach the horizon, strictly speaking. If you are orbiting the black hole at some radial coordinate r outside the horizon, you will see the effective mass of the black hole increase as soon as the infalling object falls inside your radius. (Strictly speaking, this is what you will see if the infalling object falls right by you on its way in; i.e., if its angular coordinates theta, phi are exactly the same as yours. If it falls at some other theta, phi, it may take time for the effect to propagate to you before you actually see an increase in mass.)

This is true because the gravity of the black hole (meaning, the perceived effects of gravity outside the horizon) doesn't actually come from "inside" the hole (meaning from inside the horizon). It comes from the past, from the collapsing matter that originally formed the hole. See this post (or the thread it is part of) for more:

https://www.physicsforums.com/showpost.php?p=3780798&postcount=24

An object of non-negligible mass falling into the hole works similarly; it contributes to the "mass" that is measured at a particular event in the exterior of the hole if the infalling object is anywhere in the past light cone of that event.

The gravitational or electric field of a black hole is suppose to be time-frame independent,

It is true that the "black hole is frame-independent" in the sense that the presence of an event horizon in the spacetime is frame-independent; if it's there for any observer, it's there for all observers. But in order to say that the "field" is frame-independent, you must first define what you mean by "the field". There are aspects of it that are (in an appropriate sense) frame-independent, but there are others that are not. (I'm mainly talking about the gravitational field here.)

The spacetime that the hole is in is only time independent if the black hole never has anything fall into it. If something of non-negligible mass falls into the hole, the hole changes; the spacetime the hole is in is no longer time-dependent.

 

[PAllen]

Not to single them out, but stuff like this as well as the books of people like Michio Kaku and Brian Green are confusing or conflicting.

Originally Posted by pervect View Post

and it'd approach stopping as the stationary clock got closer and closer to the event horizon.

Originally Posted by pervect View Post

There's no such thing as a stationary clock at the event horizon,

Originally Posted by pervect View Post

since the event horizon can be thought of as trapped light, any physical infalling clock, which is stationary in its own frame, will see the event horizon approaching it at the speed of light.
Originally Posted by Naty1 View Post

Can you explain what you think is 'hype'?
Here are two descriptions that reveal some of that 'character' of horizons: Kip Thorne says (Lecture in 1993 Warping Spacetime, at Stephan Hawking's 60th birthday celebration, Cambridge, England,)
The flow of time slows to a crawl near the horizon, and beneath the horizon time becomes so highly warped that it flows in a direction you would have thought was spacial: it flows downward towards the singularity. That downward flow, in fact, is why nothing can escape from a black hole. Everything is always drawn inexorably towards the future, and since the future inside a black hole is downward, away from the horizon, nothing can escape back upward, through the horizon. I get that time slows relative to an observer as distortion increases, but just as with traveling at the speed of light, it seems like that should only happen asymtotically. Stopping? From an outside observer's calculations, the in-falling object should never reach the singularity and thus the black hole would never gain mass relative to the outside observer even though the in-falling object would hit the singularity and add to it's mass? And time flowing towards the future infinitely or what?
The gravitational or electric field of a black hole is suppose to be time-frame independent, so how would you measure a change in it originating from the singularity once mass added to it especially if you can't even observer an object crossing the event horizon?

None of these are contradictory, though Thorne is at least misleading in an attempt a drama.

Let's take them one at a time:

A clock approaching the horizon appears to approach stopping ... from the point of view of an observer further away. That is all, nothing more. This says nothing about the behavior of the clock from its own point of view.

"There is no such thing as a stationary clock at the event horizon." Here, you are rather naturally confused by ambiguity in English language. Pervect is here referring to stationary in the sense of motionless relative to distant observers, not rate of time flow on a clock. The two senses of stationary juxtaposed this way lead to false perception of contradiction. Sorry about that. English is a ... <forum rules> sometimes.

Pervect's statement about the horizon moving at c past any infaller is simply true. To the infaller it simply appears as the light of prior infallers reaching them. Thus the moment they cross the horizon is the moment they can see all prior infallers. I don't see the tension with any other statements.

Now for Thorne. Unambiguously true is that the singularity is a point in time along an infaller's world line, not a spatial point. The infaller sees all prior infallers and all of the outside universe 'normally - except for frequency shift and lensing distortions' until they reach the singularity. They never see anyone else reach the singularity because they reach it (in time) before any light from someone else reaching it can get to them. Specifically, the last they see of any prior infaller is from some moments before that infaller reached the singularity.

Thorne's comments about "a direction you would have thought was spatial" and a "downwards direction" are misguided. The only one expecting this would be someone who interpreted coordinates according the letter used to name them rather than their physical characteristics. In standard Schwarzschild coordinates, the coordinate called 'r' is spacelike outside the horizon and timelike inside the horizon. This means nothing except that 'r' is a bad label for the coordinate inside the horizon. If you instead use the local Fermi-Normal coordinates of a infaller, all of this nonsense disappears.

 

[questionpost]

Correct. More specifically, the observer will never be seen to cross the event horizon.

So then we could never tell when a black hole at least is about to gain mass. We shouldn't expect any changes of the black hole if we never see anything going into it, other than perhaps its velocity. Also, what's the point of saying time stops to us at the event horizon if we can just easily calculate how matter travels past the event horizon? Why so many debates if it's that simple?

False, see my post here: https://www.physicsforums.com/showpost.php?p=3771662&postcount=10

How does the event horizon, which is symmetrical to the singularity, expand before matter has reached the singularity? Wouldn't that imply the object and the singularity are the same object if they have the same gravitational field? Why does there even need to be a bulge that straightens out? It's just something with it's own little field that clearly doesn't have the same capabilities of a black hole, I don't see how it would effect the size event horizon unless it also had an escape velocity greater than light.