New paper time, which means new movie time! In this paper with Matt Mould and Davide Gerosa and members of the @SXSProject, we confirm the existence of unstable aligned-spin binary black holes in general relativity! Paper link: https://arxiv.org/abs/2012.07147 . Settle in for a long thread!

Most objects in nature are spinning; for example, the Earth, Sun, and our galaxy are all rotating. The same applies to black holes because they are formed from dying stars that are typically rotating. Now, when two spinning black holes get together, wild things can happen!

First, if the black holes orbit each other, they lose energy to gravitational radiation, causing the orbit to shrink. This leads to even stronger radiation. This runaway process culminates in a spectacular merger of the two black holes. Credit @SXSProject for this move.

When the black holes are spinning, the simple scenario is when both spins are either "aligned" along or opposite the orbital angular momentum. In the movie below, the arrows on the BHs show the spins, while the pink arrow in the middle shows the orbital angular momentum.

For these systems, called "aligned-spin" systems, things are relatively simple: the black holes orbit in the same plane until they merge into a single black hole. The gravitational signal (shown below the black holes) also looks relatively simple.

On the other hand, if the spin directions are tilted with respect to the orbital angular momentum, it's a whole other story. In this case, the spins interact with the orbit, causing the orbital plane to wobble, or "precess". This also modulates the gravitational wave signal.

You might be wondering why the final black hole is running away. You can find out all about it here: https://twitter.com/vijay_x_varma/status/1224520601932451840

Going back to precessing binaries, because the gravitational wave signal is so different from the aligned-spin case, @LIGO and @ego_virgo can use this to learn about the spins of the black holes.

Precessing binaries are likely to form in dense environments like globular clusters, while aligned-spin binaries are likely to form in more isolated environments like galactic fields. So, (not) observing precession can tell us how the black holes formed in the first place!

So, to sum up, there are two classes of spinning binaries: aligned-spin and precessing. Notably, aligned-spin binaries are also equilibrium points, which means that a system that starts with perfectly aligned-spins will continue to be in that configuration.

Ok, now I'm finally getting to the real part of the story. Back in 2015, Davide showed that some of these binaries are actually in an unstable equilibrium: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.141102

Think of a golf ball placed on top of a basketball. If you work hard enough, you can get it to stay there. But even a small wind would make the golf ball fall off. The golf ball in this example is in an unstable equilibrium.

What Davide's work showed was that if the spin of the heavier black hole is aligned with the orbital angular momentum, while the spin of the lighter black hole is in the opposite direction, that system can suddenly start precessing if the spins are even slightly disturbed.

These are called "up-down" binaries, and have important implications: If LIGO/Virgo see a precessing binary, it doesn't necessarily have to come from a globular cluster anymore. It could have formed as an up-down binary in a different environment, and then started to precess!

Ok, now I'm really really getting to the real part of the story. Davide's calculation was based on an approximation to Einstein's general relativity called post-Newtonian theory. This method works well when the black holes are far away, but breaks down as they approach the merger

At that point, the only thing one can do is to solve Einstein's equations on a supercomputer. This is called numerical relativity and has been very successful in solving Einstein's equations for black hole mergers.

So, in this paper, we use some super-long and expensive numerical relativity simulations to look for these weird up-down binaries. And...no surprise, they are the real deal! This is what is shown in the first movie in this thread, which I will repeat below.

The purple arrow shows the spin of the heavier BH, which is along the orbital angular momentum ("up"). The orange arrow shows the spin of the lighter BH, which is "down". We start the simulation with small tilts for the spins, but as the binary evolves they become very misaligned

By the time the black holes merge (end of movie), the spins end up nearly in the orbital plane! For comparison, here are the other four configurations: up-up, down-down and down-up: . Only in the up-down case, the spins go nuts!

To sum up: We can now confirm that these up-down aligned-spin binaries do indeed become unstable and start precessing, in full general relativity! These systems may be out there in nature, and we are all really rooting for @LIGO and @ego_virgo to catch these!

If you are interested in even more details, apart from Davide's paper, you might like Matt's follow up work: https://arxiv.org/abs/2003.02281 . Matt also gets full credit for these beautiful animations!