Challenging the notion of "crossing" a black hole's event horizon

[euquila]

TL;DR Summary

I'd like to explore a perspective that challenges our usual way of talking about objects "falling into" black holes. While we know we can never directly observe anything crossing an event horizon from the outside, I want to question whether anything actually "crosses" the horizon at all - even from its own reference frame.

The conventional picture​

We often describe two perspectives of infalling matter:

1. Outside observers see the object asymptotically approach but never cross the horizon, with signals becoming increasingly redshifted
2. The infalling object supposedly experiences a finite proper time to cross the horizon

The challenge​

Here's the key insight that makes me question this picture: From the perspective of an infalling object, as it approaches the horizon, it would observe the rest of the universe's time accelerating dramatically due to gravitational time dilation. The closer it gets to the horizon, the faster the external universe would appear to evolve.

This suggests a symmetry to the horizon's unreachability:

• External observers see infalling objects approach but never cross
• Infalling objects see the universe's evolution speed up without bound as they approach

In both cases, reaching the horizon seems to require completing an infinite process. Just as external observers would need to wait an infinite time to see something cross, perhaps the infalling object would "see" the entire future evolution of the universe play out before it could reach the horizon.

The question this raises​

Should we think of event horizons as truly asymptotic boundaries that nothing can actually cross?

The case of photons​

This becomes particularly interesting when considering photons directed straight toward a black hole. Since photons don't experience proper time and always travel at c, the time dilation argument might not apply in the same way. However, incoming photons would experience increasingly extreme blue-shifting as they approach the horizon. Could this lead to some kind of limiting behavior that still prevents actual horizon crossing?

I'm interested in hearing the community's thoughts on this perspective. Am I missing something fundamental, or could this be a more accurate way to think about black hole horizons?

Note: This is a conceptual discussion that might require proper mathematical treatment to fully explore. I'm particularly interested in whether there are any published papers that have explored similar ideas.

 

[PeterDonis]

Am I missing something fundamental

Yes.

This is a conceptual discussion that might require proper mathematical treatment to fully explore.

A proper mathematical treatment shows that objects do cross the horizon and your idea is fundamentally wrong.

See this Insights article:

https://www.physicsforums.com/insights/black-holes-really-exist/

Your idea is the first misconception about black hole formation that is discussed in the article.

 

[PeterDonis]

The infalling object supposedly experiences a finite proper time to cross the horizon

Not "supposedly". This has been known as a fact since the classic 1939 paper by Oppenheimer & Snyder which showed the calculation.

 

[renormalize]

Here's the key insight that makes me question this picture: From the perspective of an infalling object, as it approaches the horizon, it would observe the rest of the universe's time accelerating dramatically due to gravitational time dilation. The closer it gets to the horizon, the faster the external universe would appear to evolve.

But suppose your infalling observer is contained inside a windowless vessel and only observes a stopwatch that he holds in his hand. With no external clues, how would he notice the approach-to and passage-of the horizon?

 

[PeterDonis]

incoming photons would experience increasingly extreme blue-shifting as they approach the horizon

Not relative to an observer far away. Relative to that observer they would experience increasing redshift.

Relative to an observer "hovering" at a constant altitude just above the hole's horizon, incoming light is blueshifted, but only as long as it is above the observer; once it falls past the observer, it starts becoming redshifted.

Could this lead to some kind of limiting behavior that still prevents actual horizon crossing?

No.

 

[PeterDonis]

perhaps the infalling object would "see" the entire future evolution of the universe play out before it could reach the horizon

No, it wouldn't. The math is clear on this.

Should we think of event horizons as truly asymptotic boundaries that nothing can actually cross?

No.

 

[Dale]

From the perspective of an infalling object, as it approaches the horizon, it would observe the rest of the universe's time accelerating dramatically due to gravitational time dilation.

The math of GR is pretty clear.

What you are describing here is not the perspective of an in falling object. What you are describing is the perspective of a series of hovering observers each closer to the horizon than the last.

But an infalling observer is not hovering. They are moving with respect to the hovering observers, and moving faster with respect to each subsequent hovering observer they pass than the previous one.

The closer it gets to the horizon, the faster the external universe would appear to evolve
…
perhaps the infalling object would "see" the entire future evolution of the universe play out before it could reach the horizon

The net result is that the infalling observer does not experience an infinite blueshift. The shift is finite. They cross the horizon in a finite proper time, and having received a finite amount of signals from the outside.