TITLE: Is black hole pattern possible in Conway's Game of Life that eats/clears everything?
QUESTION [114 upvotes]: Is black hole pattern possible in Conway's Game of Life that eats/clears the infinite universe plane ?
Formally, is there a pattern that satifies following requirements?

The pattern has finite size.
The universe plane has infinite size.
Each cell outside the pattern is initially alive or dead randomly. That is it can contain all possible patterns, including other black holes if they are possible.
For any finite region surrounding the pattern, all cells inside this region will be dead after finite generations and never back to life.

Edit:

To describe this question more intuitively: Imagine there's a circle that always expanding larger and larger and leaving the region inside it empty, no matter what patterns from the outside it collides.

Originally there was another rule: If two or more black holes collide then they will merge into a bigger black hole. It was deleted before posting because I think it's already covered by the third and the fourth rule. In addition, it's hard for me to define and describe the merging formally.

Thanks to @Vepir and @PM2Ring for mentioning related superstable configuration question. I believe this question is an extended version of the superstable configuration question which is an open problem. Because if such a black hole exists, it must be a supertable or become a supertable after finite generations.


Edit: After a bit further thinking, the metioned superstable configuration question inspired a simple but flawed answer about this question. See it below.

REPLY [6 votes]: This is not an answer to the question but a description of the properties that a potential Black Hole Pattern (BHP) could have that would invalidate some of the attempted proofs in other answers. And so, to repair those proofs, they would have to conclusively prove that there cannot exist a pattern with one or more of these properties.
Garden of Eden
Consider that for any given pattern, there is the pattern that it will produce in the next generation, its children, and then there are the set of patterns that could have produced this pattern from the previous generation, its parents. For any given pattern, there is necessarily only 1 child pattern (since GoL is deterministic), and but there is not necessarily only 1 parent pattern for a given pattern. Since many different patterns lead to extinction, it should be clear that an empty board has many potential parent patterns. However, not every pattern has any parents at all. Some patterns cannot be produced by any previous state and if they exist on the board, they can only exist a priori (from the beginning) and cannot arise later through generation evolution; these are called Garden of Edens (GoE).
Further, there are some patterns that have parents, but whose only parents are GoE patterns, that is, patterns which can only be produced by a specific GoE and by no other means. I'll call these Garden of Eden Descendants (GoE-D).
Take some GoE $g_0$ that produces some GoE-D $g_1$. And $g_1$ produces $g_2$ and so on to $g_n$. Where every $g_i$ in this chain is a pattern whose only parent is $g_{i-1}$. I'll call a chain of these $g_0$ through $g_n$, where no pattern in the chain is stable and each step in the chain is unique, a Garden of Eden Clock (GoE-C). It's a clock because if we are given an arbitrary board and on it, we find that the board contains the pattern for some $g_i$ in the chain, then we can know for certain that this board has been evolved for at most $i$ steps and no more than that. This is because if we find $g_i$, on the previous step (if there was one) we must have had $g{i-1}$ since $g_i$ has no other parents. And if we look back further, we would eventually get to $g_0$ and since $g_0$ has no parents, there cannot have been a previous step. This doesn't tell us that the board couldn't be younger than $i$. After all it could have just been initialized with $g_i$ to start with. But definitively it can be no older. For example, if we are given a board and we find on it somewhere both a $g_3$ and a $g_{40}$, we can further conclude that the $g_{40}$ pattern must not have started as a $g_0$ since the existence of the $g_3$ lets us know that the board has been evolving for at most 3 generations. So, that $g_{40}$ must have started as either a $g_{37}$, $g_{38}$, $g_{39}$ or $g_{40}$, and then evolved deterministically from there to where it is now.
Now, not all chains are going to be infinite. In fact almost all aren't. In general, a chain will at some point end and either stabilize to some static or oscillating state or will decay into another pattern that has an alternative parent pattern that could have produced it that is not a GoE-C. However, I as of yet have seen no proof that there cannot exist a GoE-C of infinite length. Also note that a GoE-C of infinite length would have to grow in size indefinitely because for any given finite bounded area, there are a finite number of possible states. And if a state was repeated, the pattern would now be oscillating, static, and/or reached a state that no longer has unique parentage.
Horizons
Here, I will describe the general potential behavior of a BHP. If there is a BHP it need not follow this exact behavior, but this is a behavior it could have.
Suppose that it starts with no empty interior that it never touches. That is, all cells within some bounding box defining the finite initial pattern must be either alive or dead just as prescribed, or else the pattern comes apart. Let 'H' mark the boundary of the pattern and '~' mark an area of the pattern where cells may or may not be alive or change their status at some point in the future.
H~~H

But at some later time, the pattern evolves to have an empty interior giving us an inner horizon inside which no cells ever become alive again, and an outer horizon, the extent to which our BHP has evolved into. Let 'h' represent the inner horizon and '_' represent a region of dead cells which will never again be brought back to life.
H~~~h___h~~~H

These two horizons will not necessarily expand at the same rate. But the outer horizon must expand faster than the inner horizon. And leaving behind this interior that is never touched ensures it meets property #4 of the original question.
Mergers and Fakes
Assume we have a BHP that evolves with the above properties over time, that the initial BHP is a $g_0$ of some infinite GoE-C chain, and that it has two horizons expanding at different rates leaving a dead region in the middle. There is the possibility that in addition to our original BHP that we have placed on the board, there could be any number of copies anywhere else on the board. When two BHPs are expanding and their outer horizons meet, if they are both true BHPs that were initialized at $g_0$, then they must either merge, or one needs to wipe through the other to preserve its own dead interior. We cannot have them merely pass through each other, or else an infinite number of BHP's on the board would have their interiors coming back to life an infinite number of times which, as pointed out in other answers, would violate rule 4.
Since GoL is Turing Complete it could be that the BHP is capable of recognizing and overriding any other horizon it finds that has higher generation number. This may involve both of their entire outer horizons merging together and comparing, and it need not be any human understandable algorithm, may differ from generation to generation, and this behavior may even be unproveable as with Turing Completeness comes the Halting Problem, and it may be that proving that lower generation numbers overriding higher generation numbers is undecidable but nonetheless true.
Now, one might postulate some "fake" COE-D. Take some real $g_i$ after it has developed a dead interior, and then add some stable shape inside the dead region. Call this new combined pattern $f_i$ which is identical to $g_i$ except for having some stable junk 'j' on the interior:
g_i:  H~~~h___h~~~H
f_i:  H~~~h_j_h~~~H

From the exterior, these would be indistinguishable. And so, if a $g_i$ encountered an $f_i$, they would either merge, never clearing each others interior, or perhaps even the $f_i$ would preserve its own junk on the interior and wipe out the interior of the $g_i$. However, consider that each pattern is a GoE-C. So, there would exist a progression:
g_0: HH
g_1: H~H
g_2: H~~H
g_3: H~~~H
g_4: H~hh~H
g_5: H~~h_h~~H
g_6: H~~~h__h~~~H
g_7: H~~~~h___h~~~~H

For $g_0$ through $g_4$ there is as of yet no interior in which to place any extra junk. So, if we want to initialize some fake on our board to start with, we'd have to start with say $g_5$ and make an $f_5$:
f_5: H~~hjh~~H

And from then on, that $f_5$ would have to evolve exactly as a $g_5$ would except for leaving the junk in the middle. This $f_5$ pattern itself would be a GoE because it has no parent at all. Unlike $g_5$ which evolves uniquely from $g_4$, this $f_5$ cannot come from some other parent since the pattern between the inner and outer horizons is already assumed to have a unique parrent. But since it's initialized as being identical to $g_5$, if it were to meet any BHP-D that was initialized as $g_0$, when they meet, our fake would appear to be 5 generations older than the real BHP-D and so the younger real BHP-D would override and clear the interior of the fake.
Conclusion
A pattern that behaved like this will all these properties would foil any proof which relied on constructing some universe with fake black holes in it because this pattern would be able to wipe out any fakes since the real thing will always be a younger generation number than any fake that could have junk in it.
Now, I think that it's highly unlikely that such a pattern with all these properties exists, but the individual properties have already shown to be exhibited by one or more real patterns:
There are space nonfillers which cover a hole empty board, activating and then deactivating forever more every cell.
There are patterns which are uniquely descended from Garden of Eden patterns.
There are patterns that fully implement Turing Machines themselves and can thus perform arbitrary logic.
And there are patterns which can cause extinction of some other patterns.
Now, I think it's highly unlikely that such a BHP with all of these properties exists. But a proper proof that one does not, would have to explicitly rule out a pattern of this type.