2024/08/31 by Daiki Saito, Tomohiro Harada, Saito, Daiki +5 · 5 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.2409.00435
openalex publication_date 2024/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We estimate the probability distribution for the spins of the primordial black holes (PBHs) that formed during an early matter-dominated era in the Universe. We employ the Zel'dovich approximation and focus on the linear-order effect of cosmological perturbations which causes the tidal torque. Assuming that the fluctuations obey Gaussian statistics, we apply the peak theory of random Gaussian variables to compute the root mean square (RMS) and the probability distribution of the non-dimensional Kerr parameter a* at their formation. The value of a* is evaluated through the angular momentum at the turn-around time. We find that the RMS a* with a given amplitude of the fluctuation δ_\rmpk decreases with the amplitude. This behavior allows us to set the threshold value of the amplitude of the fluctuation through the under-extremal condition a*<1. Then we discuss the impact of spin and anisotropic collapse on the production rate of PBHs. We find that, for σH≤ 10-3 with σ\rm H being the square root of the variance of the fluctuation at the horizon reentry, the suppression from the spin effect is dominant, while the effect of anisotropy becomes more important for σH>10-3. Since a* can be written as a function of ν:=δ_\rmpk/σ\rm H, we can obtain the probability distribution of a_*, P( a_*), through the probability distribution of ν characterized by a given power spectrum of the fluctuation. P( a_*) depends on σ\rm H and the parameter γ that characterizes the width of the power spectrum. It is shown that, in the parameter regions of our interests, substantial values of PBH spins are expected in contrast to the PBH formation in a radiation-dominated universe.