Null Infinity Waveforms from Extreme-Mass-Ratio Inspirals in Kerr Spacetime

Abstract

We describe the hyperboloidal compactification for Teukolsky equations in Kerr spacetime. We include null infinity on the numerical grid by attaching a hyperboloidal layer to a compact domain surrounding the rotating black hole and the orbit of an inspiralling point particle. This technique allows us to study, for the first time, gravitational waveforms from large-and extreme-mass-ratio inspirals in Kerr spacetime extracted at null infinity. Tests and comparisons of our results with previous calculations establish the accuracy and efficiency of the hyperboloidal layer method.

Caustic echoes from a Schwarzschild black hole

“…To avoid loss of resolution near infinity, we combine this spatial compactification with a time transformation. The time transformation is constructed requiring invariance of outgoing characteristic speeds [12,42], or equivalently, of the outgoing null surfaces in local coordinates [43,44]. Outgoing null surfaces satisfy u = t − (r + 4M log(r − 2M )) .…”

Sources of Gravitational Waves: Theory and Observations

“…Furthermore, at leading order in the computation of the radiation field, one can assume that the small test mass moves along an adiabatic sequence of geodesics of the fixed background spacetime and compute the gravitational radiation numerically solving the RWZ and Teukolsky equations [55,56,[206][207][208]. Much progress has been made in the last twenty years to evolve those equations in a robust, accurate and fast way [209][210][211][212][213][214][215][216], and compute the gravitational waveform h (1) αβ in the wave zone. Today, time-domain RWZ and Teukolsky equations can compute not only the waveform emitted during the very long inspiral stage, but also the plunge, merger and ringdown stages [216][217][218][219][220][221].…”

Gravitational waves from a plunge into a nearly extremal Kerr black hole

“…Once the complete trajectory of the smaller object is available the second step in the process is initiated. The Teukolsky equation is solved in the time-domain [16][17][18] by feeding the trajectory information into the particle source-term on the equation's right-hand-side dynamically. This computation directly generates a high-accuracy time-domain waveform for any further analysis or study.…”

“…First, a compactified hyperboloidal layer was added to the outer portion of the computational domain that allows for the extraction of the waveform data directly at null infinity [17] and completely eliminates the "outer boundary problem" which is usually a challenge for all such computations. Secondly, advances made via parallel computing, in particular, OpenCL/CUDA-based GPGPU-computing has allowed for the possibility of performing very long duration and high-accuracy computations within a reasonable time-frame.…”