I gave my second virtual talk of the lockdown today at the Gravity Exploration Institute of Cardiff University.

The talk was on three techniques for rapidly computing accurate EMRI waveforms. By combining these techniques we will be able to compute year-long EMRI waveforms in under a second. The three techniques are:

**Non-linear black hole perturbation theory.**This is needed in order to compute the post-adiabatic corrections to the waveform phase that will leave a residual error in the phase that scales with the mass ratio (so it the error in the waveform phase should be tiny for an EMRI). Our first paper on this topic presenting a result for a binary was recently published in Physical Review Letters. In this talk I also presented some exciting new (preliminary) results where we have computed the second-order (in the mass-ratio) flux for the first time. There are still many checks to go (and for some reason the l=2,m=2 mode is not working yet) but it feels great to be reaching a major goal with this long term project.**Near-identity (averaging) transformations**. Once the oscillatory pieces of the self-force are included in the inspiral models the phase space trajectory and the orbital phases oscillate (with the number of oscillations scaling with the mass ratio). Numerically computing the phase space trajectory and the phases thus becomes very slow as the integrator has to resolve tens to hundreds of thousands of small oscillations. This can be overcome using so-called near-identity (averaging) transformations, or NITs. These average out the short timescale physics to produce equations of motion that capture the correct long-term behaviour of the system but that do not oscillate on the orbital timescale. The resulting NIT’ed equations of motion can be solved in milliseconds rather than minutes. Maarten van de Meent and I published a paper on this in Classical and Quantum Gravity, which looked at the general transformation and applied to to inspirals in Schwarzschild spacetimes. Since then one of my PhD students, Philip Lynch, has explicitly derived the NIT for generic inspiral into a Kerr black hole and has a numerical model implemented for equatorial orbits in Kerr spacetime.**Fast EMRI waveforms**. To compute an EMRI waveform you need to sum over many thousands of harmonics at each time step. A straightforward implementation of this approach is quite slow, resulting in year-long waveforms that take 10s-100s of second to produce. In collaboration with Alvin Chua, Michael L. Katz, and Scott Hughes, I presented our new method for computing year-long EMRI waveforms in ~200ms. This involves a computation of a reduced-order model (ROM), neural networks and acceleration using graphics processor units (GPUs).

For those who are interested here’s a link to the slides from my talk.