Gravitational-wave parameter inference with the Newman-Penrose scalar $\psi_4$

Understand

Detection and parameter inference of gravitational-wave signals \ncor{from compact mergers} rely on the comparison of the incoming detector strain data $d(t)$ to waveform templates for the gravitational-wave strain $h(t)$ that ultimately rely on the resolution of Einstein's equations via numerical relativity simulations.

• These, however, commonly output a quantity known as the Newman-Penrose scalar $\psi_4(t)$ which, under the Bondi gauge, is related to the gravitational-wave strain by $\psi_4(t)=\mathrm{d}^2h(t) / \mathrm{d}t^2$.
• Therefore, obtaining strain templates involves an integration process that introduces artefacts that need to be treated in a rather manual way.
• By taking second-order finite differences on the detector data and inferring the corresponding background noise distribution, we develop a framework to perform gravitational-wave data analysis directly using $\psi_4(t)$ templates.