Two-body problem in curved spacetime: exploring gravitational wave transient cases

Author:

Yershov V NORCID,Raikov A A,Popova E A

Abstract

Abstract Gravitational-Wave Transient Catalogues (GWTC) from the LIGO-Virgo-KAGRA collaborations (LVC and LVK) contain almost a hundred gravitational wave (GW) detection cases. We explore them from the perspective of the two-body problem in curved spacetime, starting with the first case, GW150914, which marks the GW discovery [1]. In this paper, the LVC authors estimated the characteristic (chirp) mass of the binary blackhole system emitted this signal. Their calculation was based on Numerical-Relativity (NR) templates and presumably accounted fully for the non-linearity of GR. The same team later presented an alternative analysis of GW150914 [2], using the quadrupole post-Newtonian (PN) approximation of GR. Both analyses gave similar results, despite being based on quite different assumptions about the linearity or non-linearity of the coordinate reference frame near the GW source. Here we revisit the PN-analysis of GW150914 for which we use less noisy input GW frequencies, as we have filtered them by reading them from the time-frequency map of GW150914. As in paper [2], our result also agrees with the NR-based chirp mass value published in [1]. Additionally, we apply the PN-approximation formalism to the rest of the GWTC cases, finding that practically all of their PN-approximated chirp masses coincide with the published NR-based values from GWTC. In our view, this implies that the NR-based theory, which is currently in use for processing GW signals, does not fully account for the difference between the source and detector reference frames because the PN-approximation, which is used for the comparison, does not account for this difference by design, given the flat-spacetime initial assumptions of this approximation. We find that the basis of this issue lies in the source-to-detector coordinate transformation. For example, when obtaining the equation of motion of a coalescing binary system by integrating its energy-momentum tensor and varying the corresponding reduced action functional, the lapse and shift functions are not involved within the Arnowitt-Deser-Misner (ADM) parametrisation scheme, which is typically used for the NR-based calculation of GW waveforms A similar non-involvement of the lapse and shift functions is known to occur in the description of motion of an orbiter around a Schwarzschild blackhole. Here the GR expression for the orbital angular frequency, as seen by a remote observer, coincides with the Keplerian non-relativistic formula until the very last orbits before the plunge phase (although being fully GR-compliant). This non-involvement of the time lapse function renders the source-to-detector coordinate transformation suitable for building GW waveforms corresponding to the detector frame. However, the inverse (detector-to-source) transformation requires the derivatives of GW frequencies to be known in the source reference frame. The lack of this knowledge leads to a systematic error in the estimated chirp masses of GW sources. The corresponding luminosity distances of these sources also turn out to be overestimated.

Funder

Special Astrophysical Observatory, Russian Academy of Science

Publisher

IOP Publishing

Subject

Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics

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