Cross-posting /r/bestof (https://www.reddit.com/r/worldnews/comments/113casc/scientis...) because it really does a nice job with history and breaking down the highlights (to me at least:)

--------
Reading the paper, this is the best summary I can make. Note that I'm an engineer, not an astrophysicist.

The basic thought is that in 1963, a guy named Kerr seems to have come up with the best approximation of black holes. Many observations have been made of various black holes, and they seem to line up with his proposals. The issue is that this solution has a nasty singularity in it, which is very very extreme and doesn't really "match" the rest of nature. However, it's the only plausible explanation for the behavior seen in black holes.

People have been trying to solve this for ages. A bunch of people have different ideas for how we can resolve the singularity issue - maybe the event horizon is moving with the universe's expansion, or something funky happens to physics at high density (like how quantum mechanics gets weirder as you get smaller), or maybe the mass is somehow moved forward/backward in time and this merely appears to be a singularity from our vantage point.

However, all these are flawed because they don't take into account the fact that black holes are spinning. When you make the black hole spin, these theories all fail in one way or the other - they give the wrong results in short timescales, or they give the wrong results in long timescales.

In 2019, 2 guys named Kevin Croker and Joel Weiner demonstrated that the universe's expansion rate varies based how heavy the space next to it is. (That is a link to a summary of the paper.) This 2019 paper basically solved some questions about Einstein's equations, and importantly it also possibly answers some of the questions around singularities - even spinning ones. However, it didn't delve too deep into those questions, saying they should have a follow-up study.

This new paper is the follow-up study of that paper. It basically holds that "yes, that theory does solve the issue of singularities." They go on to say that the stress that a black hole puts on an object (its gravitational pull) can vary based on how quickly the space near the black hole is expanding.

Because the space near the black hole is expanding at different rates relative to seemingly "minor" (on the scale of the black hole) sizes, you get fluctuations to the gravitational pull that appear to be shifted through time. The paper's authors liken this to how redshift works with light; further away objects are more red than closer objects just because the light's wavelength increases with distance. The difference is that the change in gravitational pull is shifted based on time instead of distance (remembering that time is intrinsically linked to space and that we already know black holes distort time).

The paper claims that the necessary outcome of this is that you now have a physical object ("relativistic material" in science words) that must be intrinsically linked to the universe's expansion rate - as the expansion rate changes, that material also changes (or perhaps vice versa). They call this a "cosmological coupling" between everyday physics and the universe's expansion rate.

You can use the strength of this coupling (i.e. how intensely some mass is tied to the universe expansion rate) and plug it into the old 1963 Kerr equations and suddenly they work without needing weird singularities. You still get a singularity at 0 (i.e. no relation between universe expansion rate and mass), but since we know that there is a link we know that it should always be > 0 (i.e. no singularity).

They predict that for black holes you can expect that number to be about equal to 3, give or take, and such a result lines up with the 2019 paper.

Now that they have an idea of a mechanism, they can use the scientific method to see if they can experimentally replicate their hypothesis. There should be a detectable difference between the "classic" singularity approach and a "not a singularity but pretty close" approach, and they are trying to detect this by looking at how black holes gain mass.

Specifically, they're looking at supermassive black holes which seem to grow in mass as they age, even though there shouldn't be a link between time and black hole mass. Because these old galaxies are "dead", the black holes have no way to gain mass by "eating" the stuff around them, and so science currently doesn't know why these black holes appear to be growing with time - they must be growing because of some other mechanism.

The paper goes on to say they're going to do an experiment to see if that "cosmological coupling" factor actually ties in to the size of the black hole, and if the expansion of spacetime local to the black hole may explain why the black hole appears to be gaining mass when it shouldn't.

They do some experiments, blah blah blah, traditionally if there was no link between expansion and ages they "should" get the number 0 according to the 1963 model. Instead they got a value of about 3, consistently, no matter how bad the redshift was. There's a graph, it's probably closer to 2.96 than 3.14 so don't get your hopes up for some weird cosmological coincidence. They can say with 99.98% confidence that the number is not 0 like the 1963 model assumes.

They go on and say this validates their hypothesis, that a singularity explanation is not needed, and that black holes will always grow at a constant rate of about 3, using the equation a3.

They say this means black holes are made of "vacuum energy" and because of the law of conservation of energy black holes cause spacetime to dilute at a-3 , meaning this constant growth rate is causing the universe to expand (or maybe vice versa - but they appear to be related).

They do more math to prove this also holds with everything we know about universe expansion so far and that the rate of universe expansion matches what we should expect with the number of black holes we think there are.

They are careful to say this doesn't prove anything, it just demonstrates a probable link with high confidence. They give examples of further experiments that could potentially disprove their theory:

Checking the cosmic microwave background radiation to see if the numbers still line up

Checking to see if black holes reduce the energy of gamma ray bursts by an amount predicted by their theory

Checking that when two supermassive black holes collide, the result appears to gain more mass than what traditional science would expect (but would be in line with this theory, i.e. a factor of 3)

Stare at a pulsar orbiting a black hole for a decade or so and see if you can see the pulsar's orbit change according to their theory

Their theory implies that there are more massive black holes than what we observe, so someone should check to see if there's a reason why black holes aren't getting as big as this theory suggests (is there some constraint that blocks black holes from growing?)

They don't have the exact formula, only that an exact formula should exist. Someone should work it out. There is a competing theory that solves issues with quantum mechanics that may not line up with this theory; someone should check

Take more measurements and replicate this experiment to verify the numbers are correct with a larger sample size

Check quasars with a redshift of 6 and see if the math still maths

And then they say thank you and do more math. Again, I'm not an expert here so maybe I misunderstood some things, but hopefully that makes things easier to understand. It seems like the 2019 study was more impactful, and this mostly affirms the 2019 study.