Are All Black Hole Singularities Actually One and the Same?

[beeswax]

Is there any merit to the idea that all black hole singularities are in essence one and the same singularity?

 

[Dale]

Hi beeswax, welcome to PF!

Given that they can have different mass and charge and angular momentum I would see difficulty in that idea.

 

[skeptic2]

Is it not possible those quantities reside in the event horizon instead of the singularity?

 

[Dale]

The event horizon is lightlike and AFAIK nothing lightlike has either charge or mass.

 

[skeptic2]

Is not the singularity the future for everything inside the event horizon? In order for those quantities at the singularity to affect anything outside the event horizon wouldn't their effects have to travel backwards in time thus violating causality?

 

[Dale]

Why would you think that?

 

[PAllen]

It is true that the singularity is in the future of every other event inside the event horizon (there is certainly no future after it :) (for any given world line)). It is not in the past of any any world line (that is, no world line's prior light cone includes the singularity).

It is also true that an external observer never sees anything cross the event horizon.

Thus, for an external observer, the mass, charge, and angular momentum may be viewed as residing just outside the event horizon. On the other hand, an observer crossing the event horizon after the black hole has stabilized would see all mass, charge, and angular momentum attached to the singularity. This is actually rather strange in that the singularity cannot causally influence them in any way (no light or world line can go from the singularity to an infalling observer).

I don't perceive it as useful to make any speculations at all about the nature of the singularity itself.

 

[skeptic2]

Is there any merit to the idea that all black hole singularities are in essence one and the same singularity?

Without any evidence to suggest that possibility or without any new insight that such a hypothesis might offer, I don't think the idea would be taken seriously.

 

[Dale]

Thus, for an external observer, the mass, charge, and angular momentum may be viewed as residing just outside the event horizon.

I am OK with that since that would at least be timelike.

IMO, it probably is not terribly useful to worry much about localizing the mass, charge, and angular momentum.

 

[Phrak]

Thus, for an external observer, the mass, charge, and angular momentum may be viewed as residing just outside the event horizon.

I should think so--at least for the Schwarzschild solution--unless the outside observer has an infinite amount of time to wait for the critical mass to cross the critical radius, and he has assembled an infinite amount of mass to chuck into balance the Hawking radiation.

 

[beeswax]

Thanks for the replies.

The idea stems from the idea of time stopping at the singulaity, which seems to allow everything else to catch up and fall into the event horizon, regardless of how long it may take. I understand this may require a closed universe rather than an ever-expanding one, but there is still debate about whether or not the universe itself will crunch back or dissipate entirely. Also, there may be other closed universes for which Hawking radiation mass is overtaken eventually by another black hole.

In a sense, at the singularity, all time related outcomes gave already been reached, which seems to imply an intrinsic connectedness in a closed universe.

Perhaps I can ask a corollary question here and now: in a closed universe, aren't all black holes destined to become one? And if so, aren't they in effect already so, since time is on their side, so to speak? So that the apparent independence of black holes is merely an illusion of the time-bound observer? In other words, from the POV of the singularity, the end of time has already been reached, which is to say they have already merged as one?

 

[Dale]

By that same logic everything is one because it was all part of the big bang singularity and our separation is only an illusion of the time-bound observer. I just don't see the benefit of the idea.

 

[atyy]

3+1D: http://arxiv.org/abs/hep-th/9212035

4+1D: http://arxiv.org/abs/hep-th/0701035

 

[Phrak]

Perhaps I can ask a corollary question here and now: in a closed universe, aren't all black holes destined to become one?

This is my understanding--or maybe it's just an opinion.

And if so, aren't they in effect already so, since time is on their side, so to speak? So that the apparent independence of black holes is merely an illusion of the time-bound observer? In other words, from the POV of the singularity, the end of time has already been reached, which is to say they have already merged as one?

I don't think it's a good idea to talk about time from outside of time and about future events as if they are, in some metaphysical way, actually current events. It leads to all sorts of nonsensical statements, of which I've read plenty, when people confuse the natural world with their model of it where all time is perceived in the present.

I have an example statement. "In a closed universe time ends." or "In a closed universe time is finite."

These might be valid statements talking about models of the universe, but not the universe itself, where it might be true that "In a closed universe time will end."If you want to make some graphical sense of black holes with interconnected horizons and singularities try a web search on "Penrose Diagrams."