Black Hole to Other Universe: Violation of 1st Law?

[DaveL1881]

TL;DR Summary

If black holes lead to another Universe does matter falling into a black hole violate the 1st law of thermodynamics? Is matter considered "destroyed" if it no longer exists in its "home universe"?

So I am a fan of astronomy, cosmology and astrophysics from a FAR. The math is way beyond my abilities but I like to just sometimes read and think about the very small parts I am able to comprehend. So my hats off to all of you that are able to fully enjoy this stuff, you're very lucky. Embarrassingly enough, I don't even know if I'm posting this question in the right place.

So my main question is the summary. I don't have much in the way of "support material". I remember watching a program one time about Stephen Hawking. It was about a theory of his which I assume was prior to "Hawking Radiation" where if I understood correctly, Hawking was saying that matter falling into a black hole was lost forever. He was later corrected. Which I can only assume lead to "Hawking Radiation".

I've read a few times that it's theorized black holes might lead to one of many alternate universes. I was thinking about Hawking's original idea about matter falling into a black hole and if the theory about a black hole being a doorway to another Universe. If a black hole did lead to another Universe, how do you then classify that matter. I understand the whole "Matter cannot be created or destroyed" but moving it outside of the universe technically isn't either one. It straddles the line of both. From our perspective it sort of is "destroyed". It no longer exists in this universe. To the other Universe which may have different laws, matter technically while not being created is technically popping into existence in that Universe. It wasn't technically "created" as it already existed.

I get that this is complete unheard of territory and nobody will have a real answer for me. I just wanted to see what people infinitely smarter than me thought about the question.

 

[Ibix]

I'm not aware of a theory of black holes leading to other universes outside science fiction.

The simplest model of a black hole, an eternally existing non-rotating uncharged black hole called a Schwarzschild black hole, does turn out to have two exterior regions. I suppose you could call that two universes, although I wouldn't. Anyway, you can't get from one to the other even through the black hole without exceeding the speed of light, which is impossible. And they only exist in this very simple model, most probably because positing a black hole that's existed forever in an otherwise empty universe isn't particularly plausible. Realistic black holes don't have the other exterior. But that may be what Hawking was talking about. It's difficult to guess without a specific reference.

 

[kimbyd]

Summary:: If black holes lead to another Universe does matter falling into a black hole violate the 1st law of thermodynamics? Is matter considered "destroyed" if it no longer exists in its "home universe"?

So, the first law of thermodynamics is known to be non-fundamental. The very notion of a total energy in curved space-time doesn't work in general. And conservation of matter had to be violated in the very early universe for anything to exist at all.

As for what happens to the mass of a black hole when a matter enters a non-trivial black hole, such as a rotating or charged black hole which connects to a different space-time, I'm not sure. One possibility is that because it still crossed an event horizon, all information about whether the particle collided with the singularity or continued on to another universe must be destroyed, and therefore the mass of the black hole must simply increase by the amount of mass that crosses the horizon. But I'm really not sure. And quantum mechanics may well play an unknown role.

That said, I'm pretty sure this thought experiment is unphysical, as how would such a black hole have been produced in the first place?

 

[PeterDonis]

I've read a few times that it's theorized black holes might lead to one of many alternate universes.

Can you give a specific reference that is not just a pop science book or article, but an actual peer-reviewed paper? We need a specific reference that proposes a specific model on which to base discussion; without a specific model your question is not really answerable, because it's like asking what the rules would say about something when we don't know what the rules are.

 

[Haelfix]

I'm not aware of a theory of black holes leading to other universes outside science fiction.

There are known solutions that do this. Roughly one proceeds exactly as one might expect. Take the Kruskal extension of the usual black hole solution, and then glue a K = 1 FRW solution along the junction with the Einstein-Rosen bridge. Wheeler did this in the 60s, and they're sometimes known as the bag of gold solution.

The solution is viewed as pathological b/c it requires two apparently unphysical things. A past singularity (there exists no known realistic collapse solution like in the case of Oppenheimer Synder), and the strange fact that you can stick an essentially infinite amount of entropy into them, that seemingly violates various entropy bounds.

 

[PeterDonis]

Take the Kruskal extension of the usual black hole solution, and then glue a K = 1 FRW solution along the junction with the Einstein-Rosen bridge.

It looks like this construction is described in section III(b) of this paper:

https://arxiv.org/abs/0803.4212

However, I don't think this construction (even if we ignore its pathological properties) describes a black hole "leading to another universe", because there are no timelike or null paths from the exterior asymptotically flat region (the "universe" outside the black hole) to the interior of the FRW region; you can fall through the hole's horizon from the exterior region, but you'll end up in the "Big Crunch" singularity, not inside another universe that you can travel around as you please.

 

[kimbyd]

It looks like this construction is described in section III(b) of this paper:

https://arxiv.org/abs/0803.4212

However, I don't think this construction (even if we ignore its pathological properties) describes a black hole "leading to another universe", because there are no timelike or null paths from the exterior asymptotically flat region (the "universe" outside the black hole) to the interior of the FRW region; you can fall through the hole's horizon from the exterior region, but you'll end up in the "Big Crunch" singularity, not inside another universe that you can travel around as you please.

I believe the clearest one that describes this circumstance is the Reissner-Nordström space-time:
https://jila.colorado.edu/~ajsh/insidebh/penrose.html

The issue, as Haelfix mentioned, is entropy. The way I think about it is that this solution requires white holes. And white holes are unphysical because they have the wrong arrow of time: having a white hole and a black hole in the same universe is a contradiction because it means entropy is going in different directions for each.

 

[PeterDonis]

I believe the clearest one that describes this circumstance

Meaning, going through a black hole to another universe? Yes, I agree, the Reissner-Nordstrom maximal analytic extension (and the same for the Kerr spacetime equatorial plane, which looks similar) is the clearest example of that. In the destination universe, it will look like the matter from the original universe is coming out of a white hole.

(Note that these are different from the construction described in the paper I posted a link to in response to @Haelfix.)

 

[DanielJ2021]

I assumed black holes didn't actually have an interior - they were basically 2D surfaces because length contraction would make it essentially 2D at the event horizon for infalling matter? From a distance it appears like a 3D sphere but really it's a 2D surface?

 

[PeterDonis]

I assumed black holes didn't actually have an interior - they were basically 2D surfaces because length contraction would make it essentially 2D at the event horizon for infalling matter? From a distance it appears like a 3D sphere but really it's a 2D surface?

No. None of this is correct. Black holes do have an interior, which is a 4D region inside a 3D surface--the horizon is a 3D surface in spacetime. (You are thinking of it as a 2D surface in "space", but that's the wrong way to think of it if you actually want to understand what's going on; there is no invariant notion of "space" that contains the horizon--more precisely, the horizon at some instant of "time"--as a 2D surface.)