  It is speculated that a merger of two massive stellar-origin BHs in a dense
stellar environment may lead to the formation of a massive BH in the
pair-instability mass gap (50-135 Msun). Such a merger-formed BH is expected to
typically have a high spin (a=0.7). If such a massive BH acquires another BH it
may lead to another merger detectable by LIGO/Virgo in gravitational waves.
Acquiring a companion may be hindered by gravitational-wave kick/recoil, which
accompanies the first merger and may quickly remove the massive BH from its
parent globular or nuclear cluster. We test whether it is possible for a
massive merger-formed BH in the pair-instability gap to be retained in its
parent cluster and have low spin. Such a BH would be indistinguishable from a
primordial BH. We employed results from numerical relativity calculations of
black hole mergers to explore the range of gravitational-wave recoil velocities
for various combinations of merging BH masses and spins. We compared
merger-formed massive BH speeds with typical escape velocities from globular
and nuclear clusters. We show that a globular cluster is highly unlikely to
form and retain a 100 Msun BH if the spin of the BH is low (a<0.3) as such BHs
acquire high recoil speeds (>200 km/s) that exceed typical escape speeds from
globular clusters (50 km/s). However, a very low-spinning (a=0.1) and massive
(100 Msun) BH could be formed and retained in a galactic nuclear star cluster.
Even though such massive merger-formed BHs with such low spins acquire high
speeds during formation (400 km/s), they may avoid ejection since massive
nuclear clusters have high escape velocities (300-500 km/s). A future detection
of a massive BH in the pair-instability mass gap with low spin would therefore
not be proof of the existence of primordial BHs, which are sometimes claimed to
have low spins and arbitrarily high masses.
