Essential Difference Between Crossable & Non-Crossable Event Horizons

[Bandersnatch]

TL;DR

What is the requirement for an event horizon to be able to be crossed from one side vs not at all.

In a recent thread a remark was made that horizons in FLRW spacetimes are different from black hole horizons in that an observer (or a signal sent by them) can cross the black hole horizon from outside in. Whereas this is impossible in FLRW spacetimes (that have horizons). Which, yeah, duh.
But then I started thinking: what is the essential difference here? What is the requirement to make the horizon crossable from one side? So far all I could think of is that it has to do with the metric being static, but I'm just spitballing here.

 

[Ibix]

One thing to note is that the horizons in FLRW are literally everywhere: a co-moving observer just crossing our event horizon now says the same about us. Another is that things can cross FLRW horizons - but the observer who picks out a particular horizon cannot reach their own horizon. In this sense they are more like Rindler horizons than black hole horizons - they're features associated with an observer rather than invariant properties of spacetime.

 

[PeterDonis]

In a recent thread

Can you give a link?

a remark was made that horizons in FLRW spacetimes are different from black hole horizons in that an observer (or a signal sent by them) can cross the black hole horizon from outside in. Whereas this is impossible in FLRW spacetimes (that have horizons).

This is really just a quibble over which side of the horizon you call the "outside" vs. the "inside". The event horizons in FLRW spacetimes can be crossed in one direction, but not the other, just like a black hole horizon.

The real difference between a black hole horizon and the event horizons in FLRW spacetimes is that the latter are observer dependent, while the former are not. In other words, in an FLRW spacetime, each comoving worldline has its own event horizon, but in a black hole spacetime, there is just one event horizon.

What is the requirement to make the horizon crossable from one side?

FLRW spacetime event horizons are crossable from one side. See above.

 

[Bandersnatch]

Can you give a link?

It was you post, actually (and Ibix's): https://www.physicsforums.com/threa...nergy-of-a-star-collapsing-into-a-bh.1004756/ posts #8 and #9
My line of thinking might have drifted away from what you meant there, though.

The event horizons in FLRW spacetimes can be crossed in one direction, but not the other, just like a black hole horizon.

Can it?
What I mean here, is that an observer away from a BH can send a signal that reaches and passes the BH event horizon in finite time, but nothing from inside the horizon can ever reach the observer. Conversely, an observer stationary w/r to the Hubble flow can send a signal towards the EH but it'll never reach it - and, by symmetry, a signal sent from beyond the same observer's EH can't ever reach the observer.
To be clear, I don't mean that some alien today hovering near our event horizon can cross to and fro in their local space.

 

[PeterDonis]

Can it?

Yes. Any event horizon is a null surface, and any null surface can obviously be crossed in one direction; just look on a spacetime diagram of a small local patch of spacetime containing the null surface.

an observer stationary w/r to the Hubble flow can send a signal towards the EH but it'll never reach it

Wrong. The event horizon is the boundary of the region of spacetime that can send light signals to that particular comoving observer.

I suggest looking at the conformal diagram in Davis & Lineweaver's 2003 paper:

https://arxiv.org/abs/astro-ph/0310808

It's the bottom diagram of Fig. 1. Conformal diagrams are very useful for showing at a glance what regions of spacetime can or can't send light signals to what other regions of spacetime. In this case, it is obvious from the diagram that the central comoving worldline (the one considered to be the "spatial origin") can easily send light signals that cross the event horizon. (In fact, all of the other comoving worldlines will at some point cross that comoving worldline's event horizon.)

 

[Grasshopper]

Question: is the following scenario possible:

You are at rest with respect to object A and B, and all three of you are in a line, with A in the middle. Object A is within your event horizon, object B is outside your event horizon. But both you and object B are within object A’s horizon.

Gravity keeps the distance between object A and B from getting farther as the universe expands, and and it does the same for you and object.

.

.

Does that even make any sense? Because in this case, you could send a signal to A, and A could send that information to B. Kind of like a transitive property for event horizons.

 

[PeterDonis]

is the following scenario possible

No, because the concept of "event horizon" in FLRW spacetimes that have one only makes sense for comoving objects, and at most one of the three objects in your scenario can be comoving, since comoving objects do not stay at rest relative to each other.

 

[Grasshopper]

No, because the concept of "event horizon" in FLRW spacetimes that have one only makes sense for comoving objects, and at most one of the three objects in your scenario can be comoving, since comoving objects do not stay at rest relative to each other.

By comoving you mean in a frame in which the CMB is isotropic, right?

 

[PeterDonis]

By comoving you mean in a frame in which the CMB is isotropic, right?

I mean an observer who sees the CMB as isotropic. The vertical lines in the diagram I referred to are the worldlines of comoving observers.

 

[Bandersnatch]

Wrong.

I can see it now. The premise of the question was faulty. Thanks.