The future space mission LISA will observe a wealth of gravitational-wave sources at millihertz frequencies. Of these, the extreme-mass-ratio inspirals of compact objects into massive black holes are the only sources that combine the challenges of strong-field complexity with that of long-lived signals. Such signals are found and characterized by comparing them against a large number of accurate waveform templates during data analysis, but the rapid generation of templates is hindered by computing the $\sim {10}^3–{10}^5$ harmonic modes in a fully relativistic waveform. We use order-reduction and deep-learning techniques to derive a global fit for the $\approx 4000$ modes in the special case of an eccentric Schwarzschild orbit, and implement the fit in a complete waveform framework with hardware acceleration. Our high-fidelity waveforms can be generated in under 1 s, and achieve a mismatch of $\lesssim 5\times {10}^{-4}$ against reference waveforms that take $\gtrsim {10}^4$ times longer. This marks the first time that analysis-length waveforms with full harmonic content can be produced on timescales useful for direct implementation in LISA analysis algorithms.

Close

PrevNext

View figure in article

• Classical black holes
• Gravitational wave sources