Can we see matter crossing the Event Horizon with a powerful telescope?

[wsullivan]

TL;DR Summary

There is some confusion on my part what the actual reality is at the Event Horizon, since there appears to be different answers in using Kruskal-Szerrkes coordinates or
Schwartzschild coordinates. Reality does not have two answers. There is only one right one. Asked multiple times on this website, it is still an unanswered question to me: Does an object cross the event horizon in finite Earth time?

There is some confusion on my part what the actual reality is at the Event Horizon, since there appears to be different answers in using Kruskal-Szerrkes coordinates or Schwartzschild coordinates. Reality does not have two answers. There is only one right one. Asked multiple times on this website ("Physics Near Event Horizon" thread - respectfully, still unclear), one reads that saying something never crosses the event horizon in finite Earth time due to time dilation is wrong. In Schwartzschild coordinates, this is the way it comes out. But then I read that in Kruskal-Szerrkes coordinates, it does pass the event horizon in a finite period of Earth time. What seems clear is that you will not see it, because of the red shift as it approaches the event horizon. However, not being able to see something does not mean it is not happening. Yet, I read that we would be able to observe a watch starting to fall into a black hole going slower and slower the closer it got to the Event Horizon, implying that the limit of this slowing is stopping at the Event Horizon. This implies, if we watch h the watch, we will never see it cross the Event Horizon. On that thread that I mentioned, a great deal of time was spent by knowledgeable people answering questions like this, but there was no definitive answer that was not clear to me and I dare say to others.

The $64,000 question: If we had a sufficiently powerful telescope that could "see" all wavelengths no matter how red-shifted, would we see matter crossing the black hole in finite Earth time? If not, how can we observe the gravitational waves of colliding black holes (assuming this are not all due to waves generated by approaching the event horizon)? If you say that using Kruskal-Szerrkes coordinates, which are well ordered at the Event Horizon, solves the problem by saying that it will cross in finite Earth time, then how do we explain seeing the slowing and slowing of the clock as it approaches the Event Horizon or is this just a result using inadequate Schwartzscild coordinates? Incidentally, this question has driven me bunkers for years and I really really need to know the answer. Thank you for your time and knowledge.

 

[PeterDonis]

See this series of Insights articles (of which I am the author):

https://www.physicsforums.com/insights/schwarzschild-geometry-part-1/
It addresses most of the issues you raise. I'll confine myself to just a few brief comments here.

one reads that saying something never crosses the event horizon in finite Earth time due to time dilation is wrong

The qualifier "in finite Earth time" is misleading you, because "Earth time" does not have an invariant meaning for events that don't happen on Earth.

The invariant fact is that the worldline of the infalling object does cross the horizon and continue inward into the black hole. That is a fact about the spacetime geometry and a particular curve in that geometry.

However, in order to assign an "Earth time" to events on that worldline, one has to choose coordinates, and coordinates are not physically meaningful. They are just labels for events. And some choices of coordinates are simply bad ones for labeling some events. That is the case for Schwarzschild coordinates and the events on the infalling object's worldline at and below the horizon. The coordinates are simply incapable of labeling events in that region. I explain all this in more detail in the Insights article series linked to above.

If we had a sufficiently powerful telescope that could "see" all wavelengths no matter how red-shifted, would we see matter crossing the black hole in finite Earth time?

We can't see anything that happens at or below the horizon of a black hole, because light from that region can't escape. That's the definition of a black hole horizon.

However, as you yourself note, the fact that we can't see those events doesn't mean they don't happen.

If not, how can we observe the gravitational waves of colliding black holes

Because the gravitational waves come from just outside the horizon, where things can still escape.

 

[wsullivan]

I did read your articles. Perhaps you should tell me that my question does not make sense. That is the only reason I can think of for not answering it. With a sufficiently powerful telescope with unlimited ability to see any extremely red-shifted object, would I on Earth see the object crossing the event horizon? The Observer is not moving relative to the BH. Is there a Yes or No answer to this question? Since daily we read report of black holes "eating things" and" black holes merging", how could we know about the results of those things (gravitational waves detected) if they never crossed the event horizon. Unless I am totally unsophisticated, I believe the object either does cross the event horizon in the observer's finite time or it does not. It's either yes, no or no one knows.

Respectfully, please straighten me out by answering the specific question asked.

 

[PeterDonis]

With a sufficiently powerful telescope with unlimited ability to see any extremely red-shifted object, would I on Earth see the object crossing the event horizon?

I already answered that in my previous post.

 

[PeterDonis]

Also, @wsullivan, please note, you don't start a new thread to respond. You post in this one. I moved your post that you put in a new thread into this one.

 

[pervect]

A far away observer can see a sufficiently bright object get arbitrarily close to the event horizon, but will not see through a telescope an object cross it. The choice of coordinates doesn't matter to this calculation, though the ill behavior (coordinate singularities) in the Schwarzschild coordinates makes the calculations in those coordinate suspect. There are several coordinates other than Kruskal coordinates that are well behaved, though.

Since you seem to be struggling, I'm not going to answer the questions that you probably should have asked but didn't ask at this point.

 

[PeterDonis]

Since daily we read report of black holes "eating things" and" black holes merging", how could we know about the results of those things (gravitational waves detected) if they never crossed the event horizon.

Because, as I've already noted, the fact that we can't see an event doesn't mean it didn't happen. We can see objects falling into a region of space from which nothing comes out. If there were anything else but a black hole in that region of space, something would come out--maybe not the object that fell in, but light from it hitting something in the region, or other particles thrown up when it hit something. But we see nothing at all come out.

 

[Nugatory]

With a sufficiently powerful telescope with unlimited ability to see any extremely red-shifted object, would I on Earth see the object crossing the event horizon?

If your telescope is more powerful and able to see further into the infrared you will be able to see the object closer to the horizon than otherwise.

No matter how powerful your telescope is, and no matter how able to detect ever more red-shifted light it is, you will never be able to see the object cross the horizon. A better telescope just let's you see it get closer.

However: if you start with a black hole of mass $M$ and you drop an object of mass $m$ into it, you will fairly quickly have a black hole of mass $(M+m)$, even though light from the object crossing the horizon never reaches you. So even though we can’t see the object cross the horizon, there is no doubt that it does.

 

[Ibix]

With a sufficiently powerful telescope with unlimited ability to see any extremely red-shifted object, would I on Earth see the object crossing the event horizon?

An observer outside the event horizon will never see (in the literal sense of "receive light from") an object crossing the horizon. Classically, one would in principle be able to see it get closer and closer but never quite reach the horizon, although in practice it would eventually fade out of detectability. The only way to see an object cross the horizon is to follow it in yourself.

This does not stop you from declaring that, at some time by your watch, the object has fallen into the hole, assuming you can predict its proper acceleration (e.g. you know it has no engine, or its engine burns are pre-planned). There is no unique way to assign this time, and some methods of trying (notably Schwarzschild coordinates) don't work at all.

There is an unambiguous time on your wristwatch after which no signal you send can reach the object before it crosses the horizon. However, as above, you need to make assumptions about the object's trajectory after what you can currently see to determine what that is.

 

[Dale]

Reality does not have two answers. ... Does an object cross the event horizon in finite Earth time?

Although reality does not have two answers this question is not a question about reality. The relationship between Earth time and the horizon crossing is a matter of convention. So this question is a question about convention and therefore has as many answers as there are conventions.

To get questions about reality with single answers you have to propose an experiment, the outcome of an experiment is a single answer. Of course, if you go beyond the outcome of the experiment and make some interpretation of the results then that interpretation may also introduce one or more conventions and hence there may be multiple interpretations from the same experimental reality.

This is a good reality question:

If we had a sufficiently powerful telescope that could "see" all wavelengths no matter how red-shifted, would we see matter crossing the black hole in finite Earth time?

For any telescope there would be a finite lower limit of sensitivity, a lowest frequency which could be detected. That wavelength would be received in a finite time and would be detected originating from outside the horizon. There would be nothing further detected. As the low-energy sensitivity improved that time would get pushed later and later without limit and the location would get closer and closer to the horizon with a limit at the horizon.

 

[phyzguy]

I did read your articles. Perhaps you should tell me that my question does not make sense. That is the only reason I can think of for not answering it. With a sufficiently powerful telescope with unlimited ability to see any extremely red-shifted object, would I on Earth see the object crossing the event horizon? The Observer is not moving relative to the BH. Is there a Yes or No answer to this question? Since daily we read report of black holes "eating things" and" black holes merging", how could we know about the results of those things (gravitational waves detected) if they never crossed the event horizon. Unless I am totally unsophisticated, I believe the object either does cross the event horizon in the observer's finite time or it does not. It's either yes, no or no one knows.

Respectfully, please straighten me out by answering the specific question asked.

I think your question has been answered, and the answer is not that difficult to understand. The object does cross the event horizon, but a distant oberserver never sees this happening. These two statements are not contradictory.

 

[wsullivan]

I appreciate all the thoughtful answers.

 

[wsullivan]

For a more direct answer to my question, see "Gravitation", by Misner, Thorne, Wheeler; Chapter 33, Section 1.

 

[PeroK]

For a more direct answer to my question, see "Gravitation", by Misner, Thorne, Wheeler; Chapter 33, Section 1.

Ah, you were just testing us, to see whether we would be in agreement with Misner et al!

 

[wsullivan]

Ah, you were just testing us, to see whether we would be in agreement with Misner et al!

Related Thoughts:
Recap: I have always been perplexed by time dilation near the Event Horizon, essentially that there cannot be anything crossing the Event Horizon as measured by a distant non-moving observer (Earth).
I have thought up a way and I would like your comment of it. To wit: The outside gravitational effect of a hollow body is the same as the effect caused by an equally massive point mass. So, as mass accumulates close to the Event Horizon. This mass forms a massive shell. It and the central singularity combine in effect and enlarge the black hole with the new event horizon expanding to encompass the mass that used to be just outside the Event Horizon. In this way, the time dilated mass outside the EH enters the black hole in Earth time (distant observer's time). Is this analysis correct? Thank you.

 

[Dale]

Is this analysis correct?

It seems reasonable to me, but this would no longer be a Schwarzschild spacetime, you would probably have to do this numerically. So the coordinate time could be easily manipulated to give any result you want.

 

[PeterDonis]

I have always been perplexed by time dilation near the Event Horizon, essentially that there cannot be anything crossing the Event Horizon as measured by a distant non-moving observer (Earth).

See this series of Insights articles:

https://www.physicsforums.com/insights/schwarzschild-geometry-part-1/#toggle-id-1-closed
The first one (which the link will take you to) addresses the issue you raise here, but all four are worth reading if you want a better understanding of how the spacetime of a black hole works.

(Full disclosure: I am the author of the series.)

as mass accumulates close to the Event Horizon. This mass forms a massive shell

This can't happen for a shell arbitrarily close to the horizon. The shell has to be at a radial coordinate of at least $9/8$ of the horizon radius, i.e., a finite altitude above the horizon; if it gets any closer, it will collapse.

 

[PeterDonis]

In this way, the time dilated mass outside the EH enters the black hole in Earth time (distant observer's time). Is this analysis correct?

No. The distant observer will never see the shell mass cross the new horizon either. He will just see light signals from it get more and more redshifted and take longer and longer to reach him.

The correct "solution" to the issue you raise is that there is no issue that needs to be solved. The Insights article I linked to explains why.

It seems reasonable to me

It isn't, at least not with the intuitive definition of "the distant observer's time" that I think the OP is using. See above.

I agree that you can always choose coordinates such that infalling objects do cross the horizon at finite coordinate time; but that doesn't change the actual physics of light signals, which is what I believe the OP is really interested in.

 

[wsullivan]

Great Article Peter. It really helps me. Thanks.

 

[proffittcenter]

Great article, wsullivan. I have made similar points before, but less eloquently. I assume that from your respectful queries, that you have already been exposed to the Venum that querying anything in Misner et al engenders. Now, a couple of points: why are Scarzchild coordinates pathological exactly. They start at -\inf and end at +\inf and are everywhere continuous and infinitely differentiable, just like any straight line. Secondly, Kruskal-Szerrkes coordinates are not continuous at the event horizon, they are undefined. Additional assumptions need to be made.

 

[Dale]

Secondly, Kruskal-Szerrkes coordinates are not continuous at the event horizon, they are undefined

This is incorrect. I am not sure why you think this. Can you explain your reason for this belief?

 

[Nugatory]

Now, a couple of points: why are Scarzchild coordinates pathological exactly. They start at -\inf and end at +\inf and are everywhere continuous and infinitely differentiable, just like any straight line.

The pathology appears in the components of the metric tensor written in Schwarzschild coordinates; they blow up at $r=R_S$ so that we cannot use these coordinates at the event horizon. The problem goes away with a simple coordinate transformation, showing that the problem is in the coordinates and not the spacetime itself.