How does the event horizon of a blackhole know how to behave?

[Lino]

From a GR perspective, how does the event horizon of a black hole know how to behave?

Consider a simple scenario of a shell of material outside the event horizon of a black hole, in free fall. Once the material is consumed by the black hole, the event horizon will be greater, but my understanding is that in advance of the material crossing the event horizon, the horizon will "grow" to meet the infalling material at the location of the new / expanded horizon.

Is this because the material is in the future of the black hole so it (the black hole knows how to "pre-act")? If this is the case, are there other scenarios where such "pre-action" takes place?

Regards,

Noel.

 

[someGorilla]

I wouldn't see it as a "pre-action" since in order to have an action you need to have an agent. And the event horizon is not "something" that exists there. The horizon is only defined globally: there is nothing in the inventory of local events that can tell you where the horizon is located. Strictly speaking, in order to know where the horizon is, you'd need to know the entire future history of the universe. If all light signals from a given event can't reach future null infinity, that is cannot "escape", then that event is inside, otherwise it's outside. Draw a spacetime diagram - you can use any choice of coordinates. Set an event X on the horizon, and a later event Y on the now larger horizon. Now take a "test event" P more or less between X and Y and draw all the light rays originating from it (luckily there are just two on a 2d chart). If both fall back to the singularity, P is inside. The horizon, which is a lightlike wordline in your diagram, is drawn from X to Y according to this. Notice that you can't know if the light ray will escape unless you have followed it to either the singularity or infinity.
It's not that the horizon knows in advance how to move – it's rather that it is defined a posteriori according to the whole causal structure of the universe. Weird thing it is.

 

[Dale]

It's not that the horizon knows in advance how to move – it's rather that it is defined a posteriori according to the whole causal structure of the universe.

Yes, that would be the way I would answer also.

 

[Lino]

Thanks someGorilla and DaleSpam. I kind-of understand but, as with most answers, it does lead me to two related questions, if I may:

1. Should this say "have followed" instead of "haven't followed"?

... Notice that you can't know if the light ray will escape unless you haven't followed it to either the singularity or infinity. ...

2. Does the same logic (follow it to to either the singularity or infinity) apply to every location, no matter how far from the horizon - since we can never know the outcome of every light ray that might intersect with the location ... or because this is no longer a simple scenario does the logic breakdown?

Regards,

Noel.

 

[PeterDonis]

Consider a simple scenario of a shell of material outside the event horizon of a black hole, in free fall. Once the material is consumed by the black hole, the event horizon will be greater, but my understanding is that in advance of the material crossing the event horizon, the horizon will "grow" to meet the infalling material at the location of the new / expanded horizon.

Yes, this is correct.

Is this because the material is in the future of the black hole so it (the black hole knows how to "pre-act")?

The horizon isn't a "thing" that "expands". It's a global boundary that can only be defined if you know the entire history of the spacetime; it doesn't correspond directly to anything local that can be viewed as a thing expanding.

 

[Lino]

Thanks Peter.

Regards,

Noel.

 

[someGorilla]

1. Should this say "have followed" instead of "haven't followed"?

Of course. Thanks for pointing it out. Corrected.

2. Does the same logic (follow it to to either the singularity or infinity) apply to every location, no matter how far from the horizon - since we can never know the outcome of every light ray that might intersect with the location ... or because this is no longer a simple scenario does the logic breakdown?

It ought to apply everywhere, but...I reckon the standard definition of black hole as a region which is not in the causal past of future null infinity starts to get vague if we depart from the simple case of one black hole in an asymptotically flat universe. For example:
- in a universe like Gödel's you have no future (nor past) infinity and also no abrupt termination of worldlines at a singularity.
- in a collapsing universe (big crunch) all worldlines end. But it feels strange to call it a black hole! It would even mean that it can contain no other black holes.
This are just my ramblings. Hope the experts will shed some light on this.

 

[someGorilla]

This page seems to be about this:
http://www.mathpages.com/home/kmath339/kmath339.htm

 

[PeterDonis]

I reckon the standard definition of black hole as a region which is not in the causal past of future null infinity starts to get vague if we depart from the simple case of one black hole in an asymptotically flat universe.

That's right. In order for the definition to hold, there has to be a future null infinity in the first place. There isn't one in a closed universe that collapses in a big crunch. I don't think there is one in the Godel universe either, but I'd have to check references to make sure.

 

[Lino]

Thanks guys. Much food for thought!

Regards,

Noel.