Overall, this new paper highlights the power of using numerical relativity simulations as a tool to both validate and inform perturbative methods in the study of binary-black-hole dynamics and will lead to many exciting applications in the future!

The plot below shows that when we get into the weak-field, the post-Minkowskian calculations fall within the errors of the numerical relativity results which provides strong evidence that both approaches give the correct answer!

Next, we turn to the weak-field case where the black holes are barely interacting. We generated 9 new simulations where the black holes were further apart than ever simulated before. We then compared these results to those of the post-Minkowskian formalism.

We find that we can reliably extract up to second-order self-force effects. The plot below shows that with this information we can perfectly recover the scattering angles to within the numerical relativity errors, even at equal mass!

By fitting a simple polynomial to the scattering angle from the SpEC simulations we can extract the self-force which measures how much the small body's mass affects its own orbit. Image credit: NASA

We also compared our Numerical Relativity results with predictions from effective-one-body (EOB) models. In general, the models agree with the scattering angles generated with SpEC, with the plot below showing that most models differ by less than 3% in the very strong field! (6/6)

Another type of system we looked at was when the black holes have different masses. Again, we measure a difference in the scattering angle of approximately 1°. (5/6)

We also explored systems with broken symmetry. The first has black holes with spin in opposite directions. Here, for the first time, we measure the tiny difference in scattering angle of each black hole—only 0.1°! (4/6)

How do the SpEC results compare with those from other codes? The plot below shows a comparison between SpEC and the Einstein Toolkit (ETK) for a set of equal mass, non-spinning systems. Both codes agree to less than a percent! (3/6)

We simulated 60 unbound binary-black-hole encounters, covering systems with spinning black holes and mass ratios up to 10. A few examples of these trajectories are shown below. (2/6)

Black holes do have mass! In fact according to the no hair theorem they are completely described by just their mass and their angular momentum.

No special analytic solutions I’m afraid. You can get approximate analytic solutions (e.g. when they’re slowly moving and far away) but nothing generic.

Yes of course!

Essentially, in Newtonian gravity when we have two bodies we know how to solve it exactly. In General Relativity, this isn’t the case as it’s too complex. One way we can find solutions is to solve the equations by putting them on a supercomputer for a month or two. That’s what I do!