# B Physics near the event horizon

#### PeterDonis

Mentor
it can still save itself - by thrusting something towards the event horizon to propel itself upwards
We are talking about objects that free-fall radially into the black hole. They never exert any thrust, and their "orbit" is a simple radial trajectory.

This is a "B" level thread and there are enough complications already for the OP to ponder. Please do not add to them; if you want to discuss the issue you are raising about "observers" outside a black hole, please start a separate thread.

#### PAllen

Before going any further, please let me say that I have carefully read the responses and realize, much more than before, that the technical aspects of this discussion are well over my head in every way, and I am humbled that you all have taken the time to explain. I promise it is not in vain and my intention is to follow the links and try my best.

But bear with me once more, and I will try to work with PAllen's example above, where I remain at a constant arbitrary distance and drop a test body into the BH. I drop the body, start my stopwatch and observe the signal from the test body, my intent being to stop the watch when I no longer receive the signal.

Question 1: Is there a method to predict/calculate the length of time my stopwatch will run for, from the moment I drop the probe, until the time the signal ends.
This is a different question. You are asking about receiving signals from the dropped test body. I was discussing the test body receiving signals from you (the static observer). In terms of light cones, or better, causal past, future, and 'possible now', the relation of events is as follows:

For the static outside observer, there will always be events (ever closer to the horizon) in the history of the infallling test body that are in the causal past of the static obseriver. Therefore, in principle, the outside static observer can always receive information transmitted by the infalling test body from (just) outside the horizon.

However, the infalling test body's horizon crossing shifts from being in the causal future of the static external observer, to being 'possibly now and not future' at a specific finite time for the outside observer (some finite time after dropping). Some finite time after this, it is reasonable for the outside observer to consider that the horizon crossing has happened for them. All signals sent by the outside observer after this point will reach the test body only inside the horizon or not at all (because the test body has ceased to exist).
Question 2: Although I understand the signal I'm receiving will not end abruptly but instead redshift asymptotically towards wavelength = infinity as the probe approaches the event horizon, does the end of the signal (wave frequency = 0) coincide with the probe reaching the event horizon.

Again, thank you.
No, this would be when the horizon crossing becomes your causal past, which is not normally considered 'now'. Classically, this never happens for the outside observer.

#### PAllen

Of course the clock does cross the horizon at a time that can be calculated in advance. But it will happen without being observed.

For the outside observer, what happens is that the clock becomes encoded as part of the black hole's "hair" - presumably effecting its eventual decay products.
Yes, of course it won't be observed. However, there is a finite time after dropping for the outside observer such that the infaller's event horizon crossing ceases to be in the causal future. This is the point after which any signal sent by the outside observer will only arrive reach the infaller inside the horizon.

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#### .Scott

Homework Helper
Yes, of course it won't be observed. However, there is a finite time after dropping for the outside observer such that the infaller's event horizon crossing ceases to be in the causal future. This is the point after which any signal sent by the outside observer will only arrive reach the infaller inside the horizon.
So the crossing won't be in the observer's causal future or causal past. That would make it a space-like separation. A perpetual space-like separation.

#### PAllen

So the crossing won't be in the observer's causal future or causal past. That would make it a space-like separation. A perpetual space-like separation.
Yes. The key point being the horizon crossing transitions from being causal future (hasn't happened in an invariant sense) to spacelike for the outside observer a finite time (for the outside observer) after the outside observer drops the test body.

#### Staticboson

This is a "B" level thread and there are enough complications already for the OP to ponder. Please do not add to them; if you want to discuss the issue you are raising about "observers" outside a black hole, please start a separate thread.
I appreciate that observation.

When I started the thread I purposely inserted a B level with the expectation that the idealistic simplifications that work so well in explaining Modern Physics would apply to my question.

When someone asks about the twin paradox in a B level thread, one could respond by stating the practical impossibility of accelerating a rocket to near the speed of light, and explaining the rocket and astronaut inability to survive the blueshifted head-on radiation, etc., and conclude that even asking the question makes no sense because of the real-life implications. All valid and sobering concerns the OP needs to be aware of, however the essence of the question is lost.

Understanding there are many complications with actually "seeing" the falling object, the impossibility of an instrument capable of detecting a signal redshifted to near infinity wavelength, the impossibility of an observer to hover near a black hole, that the object has a "size" and therefore different portions of the object will reach the EH at different times, and many others I don't know about, my hope was to be able to break down the question down to a simple model, something along the lines of this:

A black hole event horizon, an outside observer with a clock hovering over the event horizon, and an object falling into the event horizon.

Being aware that in real life the observer will not be able to see the object any better than an observer can see his twin traveling at near C to a distant galaxy, I was wondering about the application of special relativity to the simplified model: Does the observer have to wait "forever" until the object reaches the EH, or is there a certain amount of time registered on the observer's clock when the object reaches the EH, which can be predicted/calculated based on the initial conditions.

Again, thank you all for the patience.

#### PAllen

Being aware that in real life the observer will not be able to see the object any better than an observer can see his twin traveling at near C to a distant galaxy, I was wondering about the application of special relativity to the simplified model: Does the observer have to wait "forever" until the object reaches the EH, or is there a certain amount of time registered on the observer's clock when the object reaches the EH, which can be predicted/calculated based on the initial conditions.

Again, thank you all for the patience.
I have already answered this but I will re-phrase taking you up on analogies to special relativity.

In special relativity, you know there is an issue if you use words like "when did event B happen for observer A" if A and B are not adjacent (colocated). This is because of relativity of simultaneity, which, even in special relativity, should be more generally stated as conventionality of simultaneity. That is, when, along the history of one observer, a nonadjacent event happened is totally a matter of convention within the portion of A's history such that event B has spacelike separation. Thus, you can't say B happened 'now' for you (A) if B is in your causal future or causal past, but anywhere in between you can consider it to have happened 'now'; you choose.

The one difference between special relativity and general relativity is that for inertial observers in special relativity, there is a commonly used simultaneity convention that people often pretend is 'real' rather than conventional. However, for non-inertial observers in special relativity, there isn't any standard simultaneity convention, and you literally just choose as described in the prior paragrapgh.

In general relativity, there is no standard simultaneity convention. You always have the situation of choosing by convention where along A's history B happened, subject to the constraint that B can't be in the causal future or past of your choice along A's history. Note, also, that a hovering observer has proper acceleration (thus not inertial), so even in special relativity such an observer would not have a 'standard' simultaneity convention.

With this long prelude, the hovering observer dropping a test body can easily calculate when it first becomes sensible to consider horizon crossing by the test body to have occurred, for the hovering observer. This is the point on the outside observer's history when the horizon crossing shifts from being causal future to spacelike separation. One thing you know is that after this moment for the outside observer, any signal it sends to the test body will reach the test body only inside the event horizon. What is unusual about the black hole situation is that any time after this transition for the outside observer is a sensible choice for when the horizon crossing occurred. This is because there is never a transition for the horizon crossing event becoming your causal past. Thus, there is never an end to when outside observer could consider the crossing to have happened 'now'.

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#### Staticboson

This is because there is never a transition for the horizon crossing event becoming your causal past. Thus, there is never an end to when outside observer could consider the crossing to have happened 'now'.
Admitting that most of what you wrote is well above my pay grade, I believe the last statement makes it clear:
Assuming I'm the observer, the EH crossing can never become part of my past, and the moment will never arrive when I can say the EH crossing is happening now.

I'm going to hold it here for a bit just to make sure there are no objections before I jump to the next step.

Thank you for taking the time!

#### PAllen

Admitting that most of what you wrote is well above my pay grade, I believe the last statement makes it clear:
Assuming I'm the observer, the EH crossing can never become part of my past, and the moment will never arrive when I can say the EH crossing is happening now.
Your first statement is true, your second is false, and all of my posts have tried to explain why it is false. There is a precise time for the outside observer that is the earliest they may say the crossing is happening now. However, there is no latest time they can say this.

#### Staticboson

Your first statement is true, your second is false, and all of my posts have tried to explain why it is false. There is a precise time for the outside observer that is the earliest they may say the crossing is happening now. However, there is no latest time they can say this.
"Crossing" was a poor choice of words on my part because it implies the observer having knowledge of the object being on the inside of the EH, which is impossible... "reaching" or "arriving at" is what I intended.

So I am to understand that being the observer, there will be a measurable length of time that it takes for me to see the object reach the EH, which can be predicted/calculated?

Thanks

#### PAllen

"Crossing" was a poor choice of words on my part because it implies the observer having knowledge of the object being on the inside of the EH, which is impossible... "reaching" or "arriving at" is what I intended.

So I am to understand that being the observer, there will be a measurable length of time that it takes for me to see the object reach the EH, which can be predicted/calculated?

Thanks
No, again. Seeing has nothing to do with what is happening 'now'. We see galaxies as they were e.g. a billion years ago. We assume they still exist and can compute things about their current (now) state under reasonable assumptions for some choice of simultaneity convention (cosmologists actually have a 'standard' one they mean if nothing else is specified).

You never see an object reaching the event horizon. You definitely can compute when it is no longer in your causal future, and it becomes plausible to say the crossing has happened. There is an earliest such time (the time after which any signal you send reaches the test body inside the horizon), but there is no latest such time.

#### Staticboson

No, again. Seeing has nothing to do with what is happening 'now'. We see galaxies as they were e.g. a billion years ago. We assume they still exist and can compute things about their current (now) state under reasonable assumptions for some choice of simultaneity convention (cosmologists actually have a 'standard' one they mean if nothing else is specified).

You never see an object reaching the event horizon. You definitely can compute when it is no longer in your causal future, and it becomes plausible to say the crossing has happened. There is an earliest such time (the time after which any signal you send reaches the test body inside the horizon), but there is no latest such time.
I understand that the far galaxies I see are as they were billions of years ago and not where they are now. The information about where they are now is not accessible to me because it will take billions of years for the light of where they are "now" to reach me, and by that time they will be billions of light years farther away.

But my specific wondering was exactly about about what I see, purely the perception of the observer. Imagine the observer (me) is a caveman with no idea of what is actually happening out there (not far from the truth), he just sees the object falling into the black hole. Regardless of the fact that the object will fall into the black hole in "t" time... when will the caveman see it crossing the event horizon?

#### PAllen

I understand that the far galaxies I see are as they were billions of years ago and not where they are now. The information about where they are now is not accessible to me because it will take billions of years for the light of where they are "now" to reach me, and by that time they will be billions of light years farther away.

But my specific wondering was exactly about about what I see, purely the perception of the observer. Imagine the observer (me) is a caveman with no idea of what is actually happening out there (not far from the truth), he just sees the object falling into the black hole. Regardless of the fact that the object will fall into the black hole in "t" time... when will the caveman see it crossing the event horizon?
But you keep confusing and changing terms with every post. If you are talking about seeing, you are not talking about 'now'. Seeing is about something being in your causal past, not about something happening 'now'. It is trivially true that horizon crossing event will never be in your causal past, and thus will never be seen, because this is what defines a horizon.

There is a relevant example for cosmological horizons. I believe the numbers I am going to use are ballpark correct per current models, but if not, the example can be changed to be correct.

We currently see galaxies that are 3 billion light years away, and others that are 4 billion light years away (per standard cosmological conventions). For both, we can compute their 'now' state under reasonable assumptions and conventions. For the 3 billion light year away galaxies, we will, in many billions of years, see this 'now' state. For the 4 billion light year away galaxies, we will never see this now state (due to cosmological horizon created by expansion). Is it meaningful to say that the current now for 4 billion light year away galaxies never happens because we will never see it?

#### PeterDonis

Mentor
when will the caveman see it crossing the event horizon?
He never sees it in the sense of receiving light rays from the event where it crosses the horizon. That's already been explained multiple times now.

Mentor

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