Rapid generation of fully relativistic extreme-mass-ratio-inspiral waveform templates for LISA data analysis

Our paper on rapidly computing fully relativistic EMRI waveforms is out today at arXiv:2008.06071. This is the first time that waveforms with full harmonic content can be computed on timescales useful for LISA data analysis. With our new model you can compute a year-long EMRI waveform in 10s of seconds on a CPU and in < 1s on a GPU. This is the same timing as the kludge models but without making any weak-field approximations. All the code is available in the BHPToolkit. It’s written in Python, with C++ and CUDA backends, which makes it very easy to use — see the screenshot below.


At the moment the model computes adiabatic inspirals into a Schwarzschild black hole, but the techniques used and the modular code is extensible to post-adiabatic inspirals into a Kerr black hole (watch this space). The key observation with post-adiabatic EMRI waveforms (i.e., those that include self-force corrections) is that although the waveform phase needs to be known to post-adiabatic order, the instantaneous waveform amplitudes only need to be known at leading order. Self-force corrections also add a short orbital timescale to the equations of motion. This can greatly slowdown the calculation of the inspiral but we know how to over this with either near-identity transformations or a two-timescale framework.


The main bottleneck to rapidly computing EMRI waveforms is thus interpolating the mode amplitudes and summing over thousands of modes at each time step (and each year-long waveform will have millions of time steps at LISAs sampling rate). For the interpolation we used order-reduction methods and a neural network. Neural networks are not great at high precision interpolation but we don’t need that as the error in the amplitudes does not accumulate over the inspiral. Both the neural network for the waveform amplitudes and the splines we use to sample the waveform can be evaluated extremely efficiently on a GPU. This results in year-long waveforms that can be computed in 100s of milliseconds.


The waveforms are also very accurate, with a mismatch of less than 5e-4 (relative to slow to compute high precision waveforms) across the strong-field Schwarzschild inspiral parameter space (e <= 0.7)


Finally, let me emphasize again the modular framework of the code. This should make it easy to add post-adiabatic corrections as well as environmental effects or beyond-GR/standard model physics that effect the inspiral phasing.