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 ψ4​(t) which, under the Bondi gauge, is related to
the gravitational-wave strain by ψ4​(t)=d2h(t)/dt2.
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 ψ4​(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.Comment: 18 pages, 9 Figure