LISA is considered to be launched alongside the Athena to probe the energetic astrophysical processes. LISA can determine the direction of sources for Athena’s follow-up observation. As another space gravitational wave mission, TAIJI is expected to be launched in the 2030s. The LISA-TAIJI network would provide abundant merits for sources understanding. In this work, we simulate the joint LISA-TAIJI observations for gravitational waves from coalescing supermassive black hole binaries and monochromatic sources. By using the numerical mission orbits, we evaluate the performances of sky localization for various time-delay interferometry channels. For 30 days observation until coalescence, the LISA-TAIJI network in optimal operation can localize all simulated binary sources, $({10}^7,3.3\times {10}^6)M_{\odot }$, $({10}^6,3.3\times {10}^5)M_{\odot }$, and $({10}^5,3.3\times {10}^4)M_{\odot }$ at redshift $z=2$, in $0.4{\mathrm{deg}}^2$ (field of view of Wide Field Imager on Athena). The angular resolution can be improved by more than ten times comparing to LISA or TAIJI single detector at a given percentage of population. The improvements for monochromatic sources at 3 and 10 mHz are relatively moderate in one year observation. The precision of sky localization could be improved by a factor of 2 to 4 comparing to single LISA at a given percentage of sources. For a simulated 90 days observation for monochromatic waves, the LISA-TAIJI network still represents a considerable localization advantage which could be more than ten times better.

Future space-borne interferometers will be able to detect gravitational waves at ${10}^{-3}$ to ${10}^{-1}\mathrm{Hz}$. In this band extreme-mass-ratio inspirals (EMRIs) can be promising gravitational-wave sources. In this paper, we investigate the possibility of testing the hypothesis that the small body is moving in Kerr spacetime against the alternative that the small body is moving in a parametrized non-Kerr metric by matching gravitational waveforms. EMRI snapshots from either equatorial geodesics or inclined geodesics suffer from the “confusion problem.” Our results show that, within the time scale before significant (radiation-driven) orbital evolution takes place, small and moderate deviations from the Kerr spacetime [$|{\delta }_i|<1$ in the notation of Ni, Jiang, and Bambi J. Cosmol. Astropart. Phys. 09 (2016) 014] can be discerned only when the Kerr spin parameter is extreme. In geodesic cases, most waveforms related to a non-Kerr metric can be mimicked by the waveform templates produced from a Kerr black hole. However, when radiation reaction is taken into consideration, the signals that are originally degenerate with each other will gradually separate and finally break the confusion. Depending on the mass ratio and other parameters of the system, the time needed to break the degeneracy can vary from several hours to several months.

The astrophysical origin of binary black hole (BBH) mergers remains uncertain, although many events have been observed by the LIGO–Virgo–KAGRA network. Such mergers are potentially originated in the vicinity of massive black holes (MBHs). GW190814, due to its secondary mass and mass ratio being beyond the expectations of isolated stellar evolution theories, is a promising event that has occurred in an active galactic nucleus (AGN) disk. In this model, a compact object resides in the vicinity of a merging BBH. Here we report multiple pieces of evidence suggesting that GW190814 is a BBH merging near a compact object. The orbital motion of BBHs around a third body produces a line-of-sight acceleration (LSA) and induces a varying Doppler shift. Using a waveform template that considers LSA, we perform Bayesian inference on a few BBH events with a high signal-to-noise ratio in the gravitational-wave (GW) transient catalog. Compared to the model for isolated BBH mergers, we obtain significantly higher network signal-to-noise ratios for GW190814 with the inclusion of LSA, constraining the LSA to a = 0.001 5 − 0.0008 + 0.0008 c s − 1 at a 90% confidence level. Additionally, the Bayes factor for the LSA case over the isolated case is 58/1, indicating that the LSA model is strongly preferred by the GW data. We conclude that this is the first indication showing merging BBHs are located near a third compact object.

Test of the no-hair theorem is the primary target with gravitational waves from binary black holes. In this paper, we analyze gravitational-wave data from the LIGO-Virgo-KAGRA detection of binary black-hole mergers using the Ψ_FD model, which is a non-general relativity full waveform template for arbitrary axisymmetric black holes. By analyzing two high signal-noise-ratio events, GW150914 and GW200129_065458, the no-hair theorem is tested at a significance level of 95%, which is the best constraint until now. More events and further analysis are needed to investigate the suspected deviation from the Kerr scenario found in the special event.