Dark energy may allow black holes to live in 'perfect pair' binaries

This seems highly improbable.

Sure, the distance between black holes can be calculated to have a gravitational acceleration toward each other that is offset by the expansion of space at some specific distance. And, the orbital characteristics could be included in the balance equation.

But, is that realistic? How about all the other matter that is being attracted to those black holes? And, how dynamically stable is this balance? Can the orbits be elliptical? And the authors say their "solution" does not yet even include spins.

So, I am not expecting the universe to be filled with these.
I don't think there is any value in playing with the wording.

Yes, some believe that "dark energy" is "increasing in the universe" while others believe that it is somehow offset by gravitational energy in a closed universe. The discussions I have read all seem to be inept at thinking about total energy, so my tentative conclusion is that "nobody knows".

One possibility is that there is actual energy coming into our (concept of "the") universe from places that we do not conceive. As an example, if our universe is a black hole in a larger universe than we currently recognize, matter and energy could flow into it, but (as far as we can conceive), not out of it. What would we think of that from the "inside"?
Apr 15, 2020
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This implies that dark energy is being syphoned off into gravity wave energy keeping the black holes apart. Hmmmm.... Maybe, Maybe not? What happens if the dark energy runs out in the area?
The question is,
is or how uniformly distributed is DE?

The Casimir effect is a function of insufficient distance to accommodate the arisal of quasi particles between two plates.
External arisal presses without counter balance.

Is there a/the source of DE between the black holes?
This could be a source of info on DE,
how commonly do perfect pairs of BHs occur?
1) Never
2) As statistically expected
3) More than statistically expected