# What path does matter take after entering a black hole?

## Summary:

When matter passes the event horizon does it continue in a spiral towards the center or does it take a more direct path to the center?

## Main Question or Discussion Point

Probably a silly question I thought of last night but would appreciate some clarification. Matter falling towards a black hole joins the disk spinning around the black hole slowly inching towards the event horizon with each orbit of the black hole. When matter passes the event horizon does it continue in a spiral towards the center or does it take a more direct path to the center?

I'm making some assumptions here that I have no doubt you will correct me on.

1) Matter falling towards a black hole outside the event horizon forms into a disk due to angular momentum more than being a geodesic.
2) After crossing the event horizon the geodesic effect is all that counts and the geodesic forms a straight line path direct to the center?

So to sum up if we had an outside observer that could see inside the event horizon, they would see matter spiraling towards the event horizon and then once crossing the event horizon taking a direct path straight to the center?

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Orodruin
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So to sum up if we had an outside observer that could see inside the event horizon
This is a contradiction in terms.

Also note that it is not clear what you would mean by "straight to the center". The geometry of the interior of the black hole is not Euclidean and it does not really have a "center". The singularity at $r = 0$ is more like a moment in time than a place in space as the $r$ coordinate is time-like inside the horizon.

Hi Orodruin

I was trying to very mindful about not mentioning anything to do with what the center might be, it's outside the scope of the question and I believe it will be irrelevant to the answer.

Let me try asking again slightly differently. Let's take a 5km wide black hole with it's center 2.5km away from the event horizon in all directions. Matter crosses the event horizon and travels 500m, is that 500m a spiral towards the center or a straight line towards the center?

I'm not interested about the final destination of the matter, what it might find when it gets there, or what will happen to it when it does get there. I am just interested in the path taken down to that point for the purposes of this question.

Thanks

Orodruin
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I was trying to very mindful about not mentioning anything to do with what the center might be, it's outside the scope of the question and I believe it will be irrelevant to the answer.
Your question was "does it go straight to the center?" Clearly, what is meant by "center" is highly relevant to that question.

Let's take a 5km wide black hole with it's center 2.5km away from the event horizon in all directions.
What do you mean by 5 km wide? Remember that the geometry is not Euclidean and you need to define what you mean by "center" in order for that word to hold any meaning.

Ok, maybe I am not getting this. I am just interested in what happens as soon as you pass the event horizon.

From what I have read on this forum previously (and maybe/probably interprited incorrectly,) is that the distance from the "whatever" it is that exists at the "center" to the event horizon is determined by the mass of a black hole. So the more massive the black hole, the further away the event horiszn would be from this "center." This implies an area inside the event horizon which is not the center that must be travelled through in order to reach the center. So the question is based on what happens between crossing the horizon and reaching the center.

Perhaps the term "center" is not the correct term and I should be using "final destination" instead? Or perhaps we can assume there is indeed a singularity and I should use this instead of the word "center." What happens between crossing the event horizon and travelling towards the singularity.

Your responces are leading me to believe that I have this all wrong and there is no center/singularity and eveything inside the event horizon is/acts the same, therefore making the question irrelevant.

As I understand it a singularity is a point in space and time where everything converges into a single "point." Does that "point" occupy the entire black hole? If not then there should be "something" that you need to pass through in order to reach it.

You seem to be suggesting the geometry inside the black hole cannot be thought of this way and in effect everything inside the event horizon "is" the singularity.

Ok, that's enough from me, some clarification would be welcome.

Thanks again.

256bits
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So to sum up if we had an outside observer that could see inside the event horizon, they would see matter spiraling towards the event horizon and then once crossing the event horizon taking a direct path straight to the center?
As I understand it,
For an outside observer, a singularity occurs at the event horizon, where time appears infinite.
And where an object, to the far observer, does not appear to cross the event horizon.

Yet we do know that an object can cross the event horizon ( which to the object offers no barrier to penetration ), by using other coordinates. Since spacetime acts no different just outside the horizon from just inside the horizon, ( no disjoint in physics ), for the traveler crossing through the horizon, you are asking whether the object looses its tangential velocity by virtue of the crossing. And within the black hole, how is the tangential velocity manifested, perhaps in a comparison of the trajectory of an object that fell radially directly into a black hole.

PS.As for the question, black hole questions are never silly IMO, as they are difficult to fathom, imagine, analyze,...

PeroK
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Ok, maybe I am not getting this. I am just interested in what happens as soon as you pass the event horizon.
Try this to start:

PeroK
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Or, this one:

Ibix
The singularity isn't the "centre" of a black hole - as @Orodruin notes, it's a point in time in your future (once you've crossed the horizon). That's one reason you can't avoid it - how would you avoid Tuesday morning?

The time you measure from crossing the horizon to striking the singularity (for a non-rotating uncharged black hole) depends on your trajectory, yes. The maximum, for a black hole of $K$ solar masses, is about $15K\ \mu \text{s}$. Trajectories (powered or otherwise) with a shorter survival time are possible.

In practice, tidal forces will necessarily kill you before that. Or you enter a regime where quantum gravity is important and all bets are off.

PeroK
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The singularity isn't the "centre" of a black hole - as @Orodruin notes, it's a point in time in your future (once you've crossed the horizon). That's one reason you can't avoid it - how would you avoid Tuesday morning?
I know someone who regularly avoids mornings!

Ibix
I know someone who regularly avoids mornings!
I want to die like my grandfather did, peacefully in his sleep. Not screaming in terror like his passengers.

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The singularity isn't the "centre" of a black hole - as @Orodruin notes, it's a point in time in your future (once you've crossed the horizon).
Which is also why discussions of length or radius run into trouble here. How wide is Thursday?

This is a "what do the laws of physics say would happen if we break the laws of physics" question. We can't see beyond the horizon, so "what would we see if we could" is not a well-defined question. Maybe a well-defined question could be asked, but this isn't it.

My answer - "there is no such path. Anything crossing the horizon turns into invisible pink unicorns". Prove me wrong. More importantly, describe an experiment that would prove me wrong. That might lead to an answerable question.

So....according to the video a black hole is a series of events all happening at exactly the same time at different spacial cordinates inside the event horizon. So a larger black hole just contains more events. It also suggests we do not understand why or how a black hole has mass, it's like the events "project" mass somehow or we do not really fully understand what mass is.

I'm still confused about the density of the black hole and why a smaller black hole will spaghetify you but a larger one would not. I don't understand why they do not all have the same density and cause the same effects.

Going back to my original question though, after watching this video my question is basically meaningless and irrelevant.

PeroK
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Which is also why discussions of length or radius run into trouble here. How wide is Thursday?

This is a "what do the laws of physics say would happen if we break the laws of physics" question. We can't see beyond the horizon, so "what would we see if we could" is not a well-defined question. Maybe a well-defined question could be asked, but this isn't it.

My answer - "there is no such path. Anything crossing the horizon turns into invisible pink unicorns". Prove me wrong. More importantly, describe an experiment that would prove me wrong. That might lead to an answerable question.
You could, of course, go beyond the event horizon yourself and do a experiment (if you are quick). The experiment itself can be done, but publishing the results is a different matter!

Does this mean that the predictions of GR inside the event horizon are well defined? I would lean towards saying "yes".

Ibix
Maybe a well-defined question could be asked, but this isn't it.
You can meaningfully ask what GR says about whether particles with a non-zero tangential component to their velocity as they approach the horizon continue to have a non-zero tangential component to their velocity after crossing the horizon. Yes they do. Or are there distinct trajectories inside the hole depending on your infall. Again, yes there are.

Whether or not this is testable is a nice point. It doesn't seem impossible that you could insert an object into an evaporating black hole and get it out as the hole evaporates. Whether or not it's actually possible depends on what quantum gravity actually looks like, and we don't know. And an evaporating black hole isn't a Schwarzschild black hole anyway.

Ibix
The experiment itself can be done, but publishing the results is a different matter!
Publish or perish, taken literally.

The second video linked was very useful. I have at leave some basic understand about what a Penrose diagram is now.

I'm trying to understand as much as is possible without being an academic and have already come further than I thought possible thanks to this forum.

Thank you all for your continuing patience and knowledge transfer, it is very much appreciated.

timmdeeg
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I'm still confused about the density of the black hole and why a smaller black hole will spaghetify you but a larger one would not.
This is because "spaghettification" goes with $M/R^3$. In case of a black hole the Schwarzschild radius is $R=2M$ and thus "spaghettification" goes with $1/M^2$.

DaveC426913
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It might be helpful, in an oblique way, to understand that there is nothing special about the event horizon as regards to trajectory. It's not a barrier or boundary; it is simply a geometrically-defined surface below which light (et al) cannot escape.

An infalling observer will not experience anything unusual passing through the EH; in fact he won't even know without doing some measurements and calculations (quickly!).

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It also suggests we do not understand why or how a black hole has mass, it's like the events "project" mass somehow or we do not really fully understand what mass is.
Presumably you are talking about gravitational mass. The mass of the hole is the mass of whatever has fallen in the hole.

Ibix
Presumably you are talking about gravitational mass. The mass of the hole is the mass of whatever has fallen in the hole.
...with a few caveats about exactly what you mean by "mass", before anyone takes that a bit too literally.

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why a smaller black hole will spaghetify you but a larger one would not.
That is a property of the inverse square force and not anything specific to black holes. Tides on earth are an example of "spaghettification" on a less extreme scale.

Orodruin
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A larger mass black hole will also spaghettify you according to the GR predictions - just not as you pass the event horizon or earlier.

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Whether or not this is testable is a nice point.
I don't think this is testable - your suggestions of quantum effects (Hawking radiation etc.) worry me that if you get enough down this path to see inside a horizon, you probably are far enough down this path that you can no longer think of classical trajectories. In any event, I think quantumizing the question makes it harder and not easier and so is best avoided.

Because of that, I still don't like the "looking inside the horizon" aspect for the reasons above. There are, however, some things you can say. An infalling object has linear and angular momentum, and while an outside observer can't see the post horizon trajectory, she can see that the linear and angular momentum has been transferred to the hole.

DaveC426913
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That is a property of the inverse square force and not anything specific to black holes. Tides on earth are an example of "spaghettification" on a less extreme scale.