Abstract
With 90 confirmed observations of compact binary coalescences since the first gravitational wave detection just 7 years ago, we can now optimistically draw our gaze to the horizon. The ESA-led mission Laser Interferometer Space Antenna (LISA), set to launch in 2034, promises to bring a multitude of new discoveries, extending our observable frequencies and range by orders of magnitude. This technological advancement, however, is not without its challenges. Expanding our observable volume and frequency range introduces an unprecedented number and diversity of expected signals. The biggest challenge faced by numerical relativists is the so-called "EMRI Problem". Intermediate-to-Extreme Mass-Ratio Inspirals (I-EMRIs) consist of a smaller blackhole (∼10−103M⊙) orbiting around a super massive black hole (∼105−109M⊙). To detect I-EMRIs in the LISA data stream, we must have a large representative sample of waveforms across parameter space. Unlike current detectors, LISA will be able to observe the thousands of orbits the smaller black hole takes to eventually merge with the primary black hole in I-EMRI systems. This requirement alone pushes the limit of most approximate numerical methods for waveform modelling and is prohibitively computationally expensive for the rest. I present here two novel numerical approaches for overcoming these challenges. The first, surrogate modelling, interpolates between a small selection of mass-ratio waveforms generated using point-particle perturbation theory to build a continuous set of waveforms across a wide range of mass-ratios and spins in a fraction of a second. The second method explored ere is a discontinuous Galerkin Teukolsky solver. This solver takes advantage of the discontinuity between computational sub-domains to more accurately represent the secondary black hole as aδ-function, opposed to an approximated Gaussian as previous models have done.