Gravitational-Wave Parameter Inference with the Newman-Penrose Scalar

Detection and parameter inference of gravitational-wave signals 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 ψ_{4}(t) which, under the Bondi gauge, is related to the gravitational-wave strain by ψ_{4}(t)=d^{2}h(t)/dt^{2}. Therefore, obtaining strain templates involves an integration process that introduces artifacts 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, and the impact of integration artifacts in strain templates, through the recovery of numerically simulated signals from head-on collisions of Proca stars injected in Advanced LIGO noise. Next, we reanalyze the event GW190521 under the hypothesis of a Proca-star merger, obtaining results equivalent to those previously published [Phys. Rev. Lett. 126, 081101 (2021)PRLTAO0031-900710.1103/PhysRevLett.126.081101], where we used the classical strain framework. We find, however, that integration errors would strongly impact our analysis if GW190521 was 4 times louder. Finally, we show that our framework fixes significant biases in the interpretation of the high-mass gravitational-wave trigger S200114f arising from the usage of strain templates. We remove the need to obtain strain waveforms from numerical relativity simulations, avoiding the associated systematic errors.