Extreme Gravity and Gravitational Waves

When two black holes inspiral and merge, they emit gravitational waves that have famously been detected for the first time by LIGO in 2015 [1]. These gravitational waves carry energy as well as momentum away from the black-hole binary system. The energy loss is responsible for the inspiral and eventual merger. The linear momentum radiated away, on the other hand, can impart a recoil on the black-hole system, just like the firing of a bullet imparts a recoil on the shooter. This effect follows from conservation of momentum; for black holes, the gravitational waves carry net momentum in some direction, so the black-hole emitter has to respond by moving accordingly in the opposite direction.

Figure 1. Snapshot of the gravitational-wave signal generated by an eccentric black-hole binary in the so-called superkick configuration where the black-hole spins point inside the orbital plane but in opposite directions. This snapshot shows the cross section of the wave signal around the time of the black-hole merger inside the plane perpendicular to the orbital plane. Note that the waves are stronger in the upper half than the lower half. This asymmetry corresponds to a net emission of linear momentum and a corresponding recoil of the black hole resulting from the merger. This recoil or “superkick” is illustrated in the three panels on the right which display a zoom-in of the central region at different times: the time Tm around merger (as in the large left panel) as well as 60 and 120 time units later (measured in units of the black-hole mass M). The (nearly circular) black line in these panels represents the black-hole horizon. Note that the black hole moves downwards as time progresses; this motion is the kick effect.

One of the most dramatic results of numerical relativity has been the discovery of “superkicks”, very large recoil velocities of up to 3,700 km/s that occur when the black holes start their inspiral with specific spin directions [2,3]. Such large kicks are sufficient to eject black holes from even the most massive host galaxies; the escape velocities from giant elliptic galaxies are about 1,000 km/s. This has sparked a lot of interest among astrophysical observers to look for ejected black holes, because this would have major implications for the formation history of supermassive black holes. Several candidates have been found but alternative explanations (without resorting to kicks) cannot be ruled out; see [4] for a review.

As part of our DiRAC project, we have found that even larger recoil velocities, up to 4,300 km/s are realized when the black holes inspiral on moderately eccentric (rather than quasi-circular) orbits. In general, moderate eccentricity can amplify the recoil effect by up to 25% with possible effects on the retention rate of black holes in globular clusters, second-generation populations of black-hole merger events, as well as the black-hole occupation fraction of galaxies.

[1] B. P. Abbott et al, Phys.Rev.Lett. 116 (2016) 061102, arXiv:1602.03837 [gr-qc]
[2] J. A. Gonzalez et al, Phys.Rev.Lett. 98 (2007) 231101, gr-qc/0702052
[3] M. Campanelli et al, Astrophys.J. 659 (2007) L5-L8, gr-qc/0701164
[4] S. Komossa, Adv.Astron. 2012, 364073, arXiv:1202.1977 [astro-ph]
[5] U. Sperhake et al, Phys.Rev.D 101 (2020) 024044 arXiv:1910.01598 [gr-qc]