Calderón Bustillo, JuanWong, Isaac C. F.Sanchís Gual, NicolásLeong, Samson H. W.Torres Forné, AlejandroChandra, KoustavFont, José A.Herdeiro, CarlosRadu, EugenLi, Tjonnie G. F.2026-02-112026-02-112023-12-12Calderón Bustillo, J., Wong, Isaac C. F., Sanchís-Gual, Nicolás et al. Gravitational-Wave Parameter Inference with the Newman-Penrose Scalar. Physical Review X, 13, 4, december 2023. https://doi.org/10.1103/PhysRevX.13.041048https://hdl.handle.net/10347/45828Detection 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 𝜓4⁡(𝑡) which, under the Bondi gauge, is related to the gravitational-wave strain by 𝜓4⁡(𝑡) =𝑑2⁢ℎ⁡(𝑡)/𝑑⁢𝑡2. 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 𝜓4⁡(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)], 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 errorseng©2026 American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International licenseAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Experimental studies of gravityGeneral relativityGravitational wavesAstrophysicsGravitationjournal article10.1103/PhysRevLett.126.0811012160-3308open access