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)

I’m incredibly proud to be part of this and to have my simulations turn into the first publicly available scattering and dynamical capture waveforms!

Below is a plot I made for the Einstein Toolkit Blue Book (arXiv:2503.12263) showing the waveforms SXS:BBH:3999 (scatter) and SXS:BBH:4000 (capture).

When your work Secret Santa gift link to your research

(5/7) I’m part of the effort to get the space-based Laser Interferometer Space Antenna (LISA) off the ground as an active LISA Consortium member. I’m also a former member of the LIGO collaboration.

Image courtesy of European Space Agency (ESA).

(3/7) In 2022, I started my postdoc at the Max Planck Institute for Gravitational Physics (AEI) in Potsdam, Germany. Here, I extended my work to include black hole scattering with comparable masses using Numerical Relativity as part of the @sxs-collaboration.bsky.social.

(2/7) I earned my MPhys in Physics from the University of Manchester (2018) and a PhD in Mathematical Sciences from the University of Southampton (2022). My PhD focused on using black hole perturbation theory to model small black holes scattering off supermassive black holes.

(1/7) As I’m new here I thought I should introduce myself!

My name is Olly Long and I am a researcher working on modelling the binary black hole problem in General Relativity.

Sometimes you have to go back to the basics