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Black holes (BHs) with masses between $\sim 3–5M_{\odot }$, produced by a binary neutron star (BNS) merger, can further pair up with a neutron star or BH and merge again within a Hubble time. However, the astrophysical environments in which this can happen and the rate of such mergers are open questions in astrophysics. Gravitational waves may play an important role in answering these questions. In this context, we discuss the possibility that the primary of the recent LIGO-Virgo-KAGRA binary GW230529_181500 (GW230529, in short) is the product of a previous BNS merger. Invoking numerical relativity (NR)-based fitting formulas that map the binary constituents’ masses and tidal deformabilities to the mass, spin, and kick velocity of the remnant BH, we investigate the potential parents of GW230529’s primary. Our calculations using NR fits based on BNS simulations reveal that the remnant of a high-mass BNS merger similar to GW190425 is consistent with the primary of GW230529. This argument is further strengthened by the gravitational wave-based merger rate estimation of GW190425-like and GW230529-like populations. We show that around 18% (median) of the GW190425-like remnants could become the primary component in GW230529-like mergers. The dimensionless tidal deformability parameter of the heavier neutron star in the parent binary is constrained to ${67}_{-61}^{+163}$at 90% credibility. Using estimates of the gravitational-wave kick imparted to the remnant, we also discuss the astrophysical environments in which these types of mergers can take place and the implications for their future observations. 

General relativity (GR) has proven to be a highly successful theory of gravity since its inception. The theory has thrivingly passed numerous experimental tests, predominantly in weak gravity, low relative speeds, and linear regimes, but also in the strong-field and very low-speed regimes with binary pulsars. Observable gravitational waves (GWs) originate from regions of spacetime where gravity is extremely strong, making them a unique tool for testing GR, in previously inaccessible regions of large curvature, relativistic speeds, and strong gravity. Since their first detection, GWs have been extensively used to test GR, but no deviations have been found so far. Given GR’s tremendous success in explaining current astronomical observations and laboratory experiments, accepting any deviation from it requires a very high level of statistical confidence and consistency of the deviation across GW sources. In this paper, we compile a comprehensive list of potential causes that can lead to a false identification of a GR violation in standard tests of GR on data from current and future ground-based GW detectors. These causes include detector noise, signal overlaps, gaps in the data, detector calibration, source model inaccuracy, missing physics in the source and in the underlying environment model, source misidentification, and mismodeling of the astrophysical population. We also provide a rough estimate of when each of these causes will become important for tests of GR for different detector sensitivities. We argue that each of these causes should be thoroughly investigated, quantified, and ruled out before claiming a GR violation in GW observations. 

The inspiral-merger-ringdown (IMR) consistency test checks the consistency of the final mass and final spin of a binary black hole merger remnant, independently inferred via the inspiral and merger-ringdown parts of the waveform. As binaries are expected to be nearly circularized when entering the frequency band of ground-based detectors, tests of general relativity (GR) currently employ quasicircular waveforms. We quantify the effect of residual orbital eccentricity on the IMR consistency test. We find that eccentricity causes a significant systematic bias in the inferred final mass and spin of the remnant black hole at an orbital eccentricity (defined at 10 Hz) of e0≳0.1 in the LIGO band (for a total binary mass in the range 65-200M⊙). For binary black holes observed by Cosmic Explorer (CE), the systematic bias becomes significant for e0≳0.015 (for 200-600M⊙ systems). This eccentricity-induced bias on the final mass and spin leads to an apparent inconsistency in the IMR consistency test, manifesting as a false violation of GR. Hence, eccentric corrections to waveform models are important for constructing a robust test of GR, especially for third-generation detectors. We also estimate the eccentric corrections to the relationship between the inspiral parameters and the final mass and final spin; they are shown to be quite small.