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arXiv · 2603.29790

Dark radiation from Kerr primordial black holes: the role of superradiance

Nayun Jia·Chen Zhang·Xin Zhang
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Abstract

Light primordial black holes (PBHs) that fully evaporate before Big Bang Nucleosynthesis (BBN) produce dark radiation (DR) via Hawking radiation of gravitons, contributing to the effective number of relativistic species $\Delta N_{\rm eff}$. If the particle spectrum contains a beyond-the-Standard-Model (BSM) boson with Compton wavelength comparable to the black hole (BH) gravitational radius, superradiant instability extracts angular momentum from the BH into a bosonic cloud, whose gravitational wave (GW) emission contributes an additional source of DR. By simultaneously evolving the BH mass and spin, superradiant mode occupation numbers, comoving entropy and cosmological energy densities in an expanding early-universe background, we find that superradiance generically suppresses $\Delta N_{\rm eff}$: by extracting angular momentum before Hawking radiation can convert it into gravitons, superradiance starves the dominant dark-radiation channel. The GWs emitted by the superradiant cloud can partially compensate this loss, but only when the superradiant and BH evaporation timescales are comparable; otherwise the cloud GWs are emitted too early and diluted by cosmological expansion. The results imply that existing $\Delta N_{\rm eff}$ bounds on PBH mass and spin derived without superradiance must be revisited if BSM bosons are present in the particle spectrum.

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Nayun Jia, Chen Zhang, Xin Zhang. 2026-03-31. Dark radiation from Kerr primordial black holes: the role of superradiance. https://arxiv.org/abs/2603.29790

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