Can't Avoid Invoking Preferred Frame: A Look at Free Falling Into a Black Hole

[Grinkle]

TL;DR Summary

I have come to realize that all of my pondering of GR has led me to consistently invoke a preferred frame when I consider an event horizon. Is that a barrier to my understanding GR at a lay person level?

Take this video as an example. Its an attempt to humanize the hypothetical experience of free falling into a black hole.When I consider this video, the proper time of the traveler in crossing the EH is intuitively preferred for me, and the proper time of an observer on the spaceship as they wait to see the traveler cross the EH is illusory. My instinct tells me that in fact, there is a preferred frame where the traveler is dead in one hour (more or less) of proper ship time even though an observer on the ship can do no experiment to confirm this, and all GR is telling me is that there is no experiment that can be done by a ship-bound observer to confirm the fact of the travellers demise by spagettification.

Is this a question of interpretation and not a question of GR per se? I think I am mentally de-coupling time from space-time somehow in this thinking, but I can't get past it. I would like a perspective where both observers are correct but I am struggling to get there. I think the traveller is correct and the ship-bound observer is just unable to observe what has happened.

In SR, as far as I know at least, I don't have the same problems - I can get to the point where my intuition agrees that two observers moving relative to each other each see the others clock moving slower and both are correct.

 

[PAllen]

Well let’s look at things that don’t depend on which observer you “like”. Invariant things.

The infaller takes a short finite proper time to cross the horizon and reach the singularity. The infaller can continue to receive signals from the rocket at and beyond horizon crossing until they reach the singularity. No signal sent by the infaller will ever reach the rocket if it was sent at or after horizon crossing. The infaller’s (causal) past is infinite in extent (in an idealized model) and uncensored (assuming there is only one BH). However, the infaller’s future is highly circumscribed, and includes none of the exterior and less and less of the interior as it proceeds to “death”.

These are all invariant facts (per GR), and the rocket would not disagree on any of them, even though it can’t observe some of these facts.

The causal evolution of the rocket is that its future is uncensored, and always includes events inside the horizon up to the singularity. Its acausal region (neither future nor past, possibly “now”) comes to include the events on the horizon and whole interior at a particular moments of the rocket’s history, in the case of a BH formed from collapse. At this point, it is sensible for the rocket to consider that the horizon currently exists. However the rocket’s past is censored to never include the horizon or interior. Note that for a given moment of the rocket’s history, the future events on the horizon are different from the possibly “now” events on the horizon.

There is no need to look at any of this as features of a “frame”. All these facts are simply true features of the universe, per GR. This is really no different from the obvious expectation that someone in a distant galaxy sees a different collection of galaxies than we do.

 

[PeterDonis]

My instinct tells me that in fact, there is a preferred frame where the traveler is dead in one hour (more or less) of proper ship time

As @PAllen says, this isn't a "preferred frame", it's an invariant fact. Just as if a ship on Earth that's over your horizon collides with something, that collision is an invariant fact even though you personally can't see it.

 

[PeroK]

In SR, as far as I know at least, I don't have the same problems - I can get to the point where my intuition agrees that two observers moving relative to each other each see the others clock moving slower and both are correct.

SR is conceptually simpler because all inertial reference frames can assign coordinates to all events in spacetime. In other words, IRFs are global.

It is a conceptual hurdle in GR that inertial reference frames are not global and that, generally, coordinate systems cannot assign coordinates to all events. In this case, you'd like to think that the events of the object crossing the EH and reaching the singularity can be described using the time on a clock far from the black hole. They can't.

Many treatments of SR (especially popular ones) over-emphasise the role of an "observer"; and, especially the role of light signals from an event reaching that observer. Even in SR, it's important to dissociate the physics from what an individual observers "sees".

In this case, the physicist a long way from the black hole is not constrained to study the problem in only one coordinate system - nor are they obliged to consider only events from which light signals will eventually reach them. They may develop a complete understanding of all the spacetime events in this case, including the events that cannot be mapped to a time on their local clock.

That there are such events may be conceptually unnerving, but understanding that is part of the process of understanding GR and more complicated spacetimes.

 

[Grinkle]

Thanks for the responses / help. I am thinking that my discomfort is probably around not having considered or really comprehended the below.

in GR that inertial reference frames are not global and that, generally, coordinate systems cannot assign coordinates to all events.

All the comments are quite helpful for me, and I am once again feeling very privileged to have access to this community.

 

[PAllen]

In this case, the physicist a long way from the black hole is not constrained to study the problem in only one coordinate system - nor are they obliged to consider only events from which light signals will eventually reach them. They may develop a complete understanding of all the spacetime events in this case, including the events that cannot be mapped to a time on their local clock.

While this must be expected in the general case in GR, for a Schwarzschild BH there are many ways to associate horizon and interior events to distant clock times. For example, simply choose some distant observer, use a foliation like Kruskal or Lemaitre, and then assign times to the slices using the distant observer’s clock.

 

[PAllen]

While this must be expected in the general case in GR, for a Schwarzschild BH there are many ways to associate horizon and interior events to distant clock times. For example, simply choose some distant observer, use a foliation like Kruskal or Lemaitre, and then assign times to the slices using the distant observer’s clock.

I’ll add that this does not really work for a Kerr BH, if you try to include the region with CTC. You would have a purported simultaneity surface with the feature that it contains distinct events, e1 and e2, such that e2 is in the causal future of e1. I believe there are no spacelike, achronal surfaces possible in the Kerr spacetime that include much of the interior as well as the exterior.