The appearance of a merging binary black hole very close to a spinning supermassive black hole

The mass and distance of a binary black hole (BBH) are fundamental parameters to measure in gravitational wave (GW) astronomy. It is well-known that the measurement is affected by cosmological redshift, and recent works also showed that Doppler and gravitational redshifts could further affect the result if the BBH coalesces close to a supermassive black hole (SMBH). Here we consider the additional lensing effect induced by the nearby SMBH on the measurement. We compute the null geodesics originating within 10 gravitational radii of a Kerr SMBH to determine the redshift and magnification of the GWs emitted by the BBH. We find a positive correlation between redshift and demagnification, which results in a positive correlation between the mass and distance of the BBH in the detector frame. More importantly, we find a higher probability for the signal to appear redshifted and demagnified to a distant observer, rather than blueshifted and magnified. Based on these results, we show that a binary at a cosmological redshift of z(cos) = (10(-2)-10 (-1)) and composed of BHs of (10-20) M-circle dot could masquerade as a BBH at a redshift of z(cos) similar to 1 and containing BHs as large as (44-110) M-circle dot. In the case of extreme demagnification, we also find that the same BBH could appear to be at z(cos) > 10 and contain subsolar-mass BHs. Such an effect, if not accounted for, could bias our understanding of the origin of the BHs detected via GWs.

Automated summary

The mass and distance of a binary black hole (BBH) are important parameters to measure in gravitational wave (GW) astronomy. The measurement can be affected by cosmological redshift, Doppler and gravitational redshifts, and the lensing effect of nearby supermassive black holes (SMBHs). This study finds that there is a positive correlation between redshift and demagnification, and a higher probability for the signal to appear redshifted and demagnified. If not accounted for, this effect could bias our understanding of the origin of the detected black holes via GWs.