Gravitational-wave parameter inference with the Newman-Penrose scalar

Current detection and parameter inference of gravitational-wave signals relies 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 ψ 4 ( t ) which, under the Bondi gauge, is related to the gravitational-wave strain by ψ 4 ( t ) = d 2 h ( t ) / 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 ψ 4 ( t ) templates. We first demonstrate this formalism through the recovery numerically simulated signals from head-on collisions of Proca stars injected in Advanced LIGO noise. Next, we re-analyse the event GW190521 under the hypothesis of a Proca-star merger, obtaining results equivalent to those in Ref. [1], where we used the classical strain framework. Our framework removes the need to obtain the strain from numerical relativity simulations therefore avoiding the associated systematic errors.

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