Available data on the chirp mass distribution of the coalescing black hole binaries in O1-O3 LIGO/Virgo runs are analyzed and compared statistically with the distribution calculated under the assumption that these black holes are primordial with a log-normal mass spectrum. The theoretically calculated chirp mass distribution with the inferred best acceptable mass spectrum parameters, M0=17 M⊙ and γ=0.9, perfectly describes the data. The value of M0 very well agrees with the theoretically expected one. On the opposite, the chirp mass distribution of black hole binaries originated from massive binary star evolution requires additional model adjustments to reproduce the observed chirp mass distribution.

Primordial stellar-mass black holes, which may contribute to dark matter and to the observed LIGO binary black hole coalescences, are expected to be born with very low spins. Here we show that accretion mass gain by the components of a primordial black hole binary from the surrounding matter could lead to noticeable spins of the components prior to the coalescence provided high initial orbital eccentricities.

Modern astrophysical methods for determining spins of rotating stellar-mass black holes in close binaries and of supermassive black holes in active galactic nuclei are briefly discussed. Effective spins of coalescing binary black holes derived from LIGO/Virgo gravitational wave observations are specially addressed. The effective spins of coalescing astrophysical binary black holes and black holes with neutron stars are calculated for two plausible models of black hole formation from stellar core collapses (without or with an additional fallback from the stellar envelope) taking the stellar metallicity and star formation rate evolution in the Universe into account. The calculated distributions are consistent with the reported LIGO/Virgo observations. Distributions of the effective spins expected in yet undiscovered neutron star – black hole binaries have been calculated. The effective spins of primordial coalescing stellar-mass black holes can reach a few percent due to the accretion spin-up in a cold external medium.

Modern astrophysical methods of determination of spins of rotating stellar-mass black hole in close binaries and of supermassive black hokes in active galactic nuclei are briefly discussed. Effective spins of coalescing binary black holes derived from LIGO/Virgo gravitational wave observations are specially addressed. We consider three types of coalescing binaries: double black holes, black hole -neutron star binaries and primordial double black holes. The effective spins of coalescing astrophysical binary black holes and black holes with neutron stars are calculated for two plausible models of black hole formations from stellar core collapses (without or with additional fallback from stellar envelope) taking into account the stellar metallicity and star formation rate evolution in the Universe. The calculated distributions do not contradict the reported LIGO/Virgo observations. The effective spins of primordial coalescing stellar-mass black holes can reach a few per cent due to accretion spin-up in the cold external medium.1 Here we use geometrical units G = c = 1 unless stated otherwise.

We briefly discuss a possible cosmological implication of the observed binary black hole mergings detected by LIGO-Virgo-Kagra collaboration (GWTC-3 catalogue) for the primordial black hole (PBH) formation in the early Universe. We show that the bumpy chirp mass distribution of the LVK BH+BH binaries can be fit with two distinct and almost equal populations: (1) astrophysical mergings from BH+BH formed in the modern Universe from evolution of massive binaries and (2) mergings of binary PBHs with initial log-normal mass distribution. We find that the PBH central mass (M c 30M ) and distribution width derived from the observed LVK chirp masses are almost insensitive to the assumed double PBH formation model. To comply with the observed LVK BH+BH merging rate, the CDM PBH mass fraction should be f pbh ∼ 10 −3 but can be higher if PBH clustering is taken into account.