Exact Radiation Boundary Conditions and Near-to-Far Field Teleportation for the Time-Domain Teukolsky Equation

A wide range of theoretical and astrophysical problems—including modeling gravitational waves from extreme mass ratio inspirals (EMRIs)—require the accurate numerical solution of the time-domain Teukolsky equation for spin weight s=−2 in Boyer–Lindquist coordinates. However, long-time evolution of this equation is notoriously hampered by unphysical reflections from the outer boundary and by slowly growing spurious modes that contaminate the physical waveform. We develop and implement exact radiation outer boundary conditions (ROBCs) for the Bardeen–Press equation (the a=0 limit of the Teukolsky equation), which make the outer boundary fully transparent without the need for coordinate compactification or auxiliary transformations. In addition, we construct near-field-to-far-field teleportation kernels that allow the waveform to be evaluated directly at future null infinity from data recorded at a finite radius. Our results demonstrate that these boundary treatments eliminate unphysical late-time growth, yield the correct asymptotic decay rates, and enable efficient, long-duration time-domain simulations relevant to EMRI waveform modeling and other black hole perturbation problems.