BHPWAVE: An adiabatic gravitational waveform model for compact objects undergoing quasi-circular inspirals into rotating massive black holes

We present {bhpwave}: a new Python-based, open-source tool for generating the gravitational waveforms of stellar-mass compact objects undergoing quasi-circular inspirals into rotating massive black holes. These binaries, known as extreme-mass-ratio inspirals (EMRIs), are exciting mHz gravitational wave sources for future space-based detectors such as the Laser Interferometer Space Antenna (LISA). Relativistic models of EMRI gravitational wave signals are necessary to unlock the full scientific potential of mHz detectors, yet few open-source EMRI waveform models exist. Thus we built {bhpwave}, which uses the adiabatic approximation from black hole perturbation theory to rapidly construct gravitational waveforms based on the leading-order inspiral dynamics of the binary. In this work, we present the theoretical and numerical foundations underpinning {bhpwave}. We also demonstrate how {bhpwave} can be used to assess the impact of EMRI modeling errors on LISA gravitational wave data analysis. In particular, we find that for retrograde orbits and slowly-spinning black holes we can mismodel the gravitational wave phasing by as much as $\sim 10$ radians without significantly biasing EMRI parameter estimation.