I Inside the Schwarzschild horizon

[jbriggs444]

Would it be correct to say that it is impossible to observe from the outside any phenomena inside the event horizon, and also from the inside any phenomena happening closer to the center of the black hole than you are?

Mostly correct.

You can observe stuff that is closer to the singularity than you are. It is just that by the time you observe it, you'll be closer to the singularity than the object you observed was when you observed it.

The above description is not quite right either. It is just my own intuitive picture.

It is tempting to picture a black hole in terms of familiar 3-D geometry with a center that you approach in space. But that is not quite right. The singularity is not a position in space. It is more like a moment in the future. You cannot escape it any more than you can escape tomorrow.

[Mentors' note: This thread was forked off from an altogether unrelated thread]

 

[Buzz Bloom]

It is tempting to picture a black hole in terms of familiar 3-D geometry with a center that you approach in space. But that is not quite right. The singularity is not a position in space. It is more like a moment in the future. You cannot escape it any more than you can escape tomorrow.

Hi jbriggs:

Thank you for this insight. I would much appreciate a citation to a reference about space-time inside an event horizon and the way phenomena behave there. I would like to improve my understanding of this topic.

Regards,
Buzz

 

[jbriggs444]

Thank you for this insight. I would much appreciate a citation to a reference about space-time inside an event horizon and the way phenomena behave there. I would like to improve my understanding of this topic.

I do not have much to offer in the way of references. Just a few observations.

A black hole is a vacuum solution to the Einstein field equations. That means that it is nothing but vacuum everywhere. [If we add an observer, we make the tacit assumption that the observer's mass is negligible]

Space-time is a four dimensional pseudo-Riemannian manifold. That means that no matter where you go, space time will always behave locally in the familiar way with three orthogonal dimensions of space and one dimension of time.

The definition of a manifold requires that it be an open set that is coverable everywhere by cartesian coordinate systems. Roughly speaking, that means that no matter where you are in the manifold, there is still more manifold in every direction. There are no sharp edges. An intuitive picture would be to think of the open interval of points between 0 and 1 but excluding 0 and 1. By contrast the closed interval from 0 to 1 inclusive would not qualify to be a manifold.

There is a singularity in a black hole. The singularity is similar in some ways to the zero end of the open interval (0,$\infty$). Zero is not part of the interval. Similarly, the singularity is not part of the manifold. But points within the manifold are arbitrarily close.

As you get closer and closer to the singularity, space-time curvature is more and more intense. So tidal stretching and squishing will exceed any finite value.

Not sure if any of that helps.

 

[Nugatory]

Thank you for this insight. I would much appreciate a citation to a reference about space-time inside an event horizon and the way phenomena behave there. I would like to improve my understanding of this topic.

@PeterDonis's collection of Insights articles on the Schwarzschild geometry would be a good start.

 

[pervect]

Andrew Hamilton wrote a bit about this, I'm not sure how clear it is. It isn't a peer reviewed paper, but Hamilton has written some peer reviewed papers.

<link to source>

The small white dot indicates our point of entry through the horizon. Remarkably, the Schwarzschild surface, the red grid, still appears to stand off at some distance ahead of us. The white dot is actually a line which extends from us to the Schwarzschild surface still ahead, though we only ever see it as a dot, not as a line. The dot-line marks the formation of the Schwarzschild bubble (see below), and our entry into that bubble. Persons who fell through the Schwarzschild surface at this precise point before us would lie arrayed along this dot-line. At this instant, as we pass through the horizon into the Schwarzschild bubble, we see all the other persons who passed through this location before us also pass through the horizon into the bubble.

The main web pages for Hamilton start at https://jila.colorado.edu/hamilton/black-holes/research-black-holes, which will take you to the older web page (where this excerpt I quoted is from), and also a newer web page that I haven't looked at much.

I' d like to rephrase some of these ideas a bit differently. Suppose you were in a space ship, and you were watching the bow as the ship crossed the event horizon. At the instant the bow of the ship entered the black hole, a light flashes in the bow. What would you see in the stern of the ship?

You would see the flash as normal, at least for a reasonably size ship. I suppose it's likely that if you had a very, very long ship, , you might see some distortions of the image and red-shifting due to tidal forces. I haven't seen anybody describe the details of this.

What would be happening from the Schwarzschild perpsective, though, is that the flash of light would be trapped at the horizon, you would catch up to it and the flash of light would hit your eye at exactly the instant your eye reached the horizon. Your brain would process the images as usual, and through the usual mechanics of perception you'd perceive the flash. The process by which your brain processes the visual input from your eye takes time of course, but that starts to get into biology , rather than physics.

 

[Orodruin]

You can observe stuff that is closer to the singularity than you are.

Care must be taken to clarify what you mean by ”close” here. The singularity is more like a moment in time than it is a position in space.