Numerical relativity · early Universe · open lab notebook

Primordial black holes before reheating

Could all of the dark matter be black holes with the mass of an asteroid, 10¹⁹–10²⁰ g? Such holes can only have formed in the first moments, if after inflation the Universe spent a while filled with the cold "dust" of a heavy field. We compute this collapse in full general relativity — from the exact solution to three-dimensional particle simulations.

The 10-minute version Results Computation log

μ_th(D)

The whole project comes down to one number: how strong the initial curvature peak μ must be to collapse into a black hole before reheating — the moment D when the dust era ends and matter turns into radiation. The lower the threshold, the more holes form and the smaller the seed inflation has to provide.

What we have so far

Spherical, cold Vlasov, GRμ_th ≈ 0.039 / 0.019 / 0.0086

Thresholds for deadlines D = 100 / 300 / 1000 t_H. The map is converged in grid and shell number; there is no floor down to μ = 0.01.

Results, 1D

3D GR with particles, e = 0±0.01 t_C(0)

Our own 3D module PBHVlasov reproduces the horizon growth of the exact LTB solution and of the 1D code from 0.1 to 0.6 M_H.

Stage 2

Non-spherical peak, e = 0.2, μ = 0.3τ = 2.09 t_C(0)

The horizon is born almost twice as late in the proper time of the matter (sphere: 1.13), but straight away with ≈ 1 M_H.

Stage 1b

Small-scale kicks≈ 0.03 c

If particles receive velocities of ≈ 0.03 c at turnaround, there are no spherical PBHs at μ ≤ 0.05 within 300 t_H: the threshold is then set by substructure, not by the peak's gravity.

Dispersion

Profile shapea first-order effect

A steep lognormal peak (Δ = 0.5) forms its horizon only at 1.5 t_C(0) instead of 1.1 — or not by 1.8; a flat core traps 0.8 M_H at once.

Profiles

A scalar field instead of particlesbounce

At affordable m/H a coherent field bounces off the centre (Kaup limit) — which is why the physical regime q ≥ 10⁹ is computed with Vlasov particles.

Stage 1

running A μ grid for non-spherical peaks

Three early-start 3D runs are queued on the CCX43 server, about a day each: μ = 0.1 at e = 0.2, then μ = 0.05 at e = 0.2 and at e = 0.13. They will show whether realistic (non-spherical) peaks become black holes before deadlines of 100–300 t_H.

Sections

ExplainedWhat we compute and why it matters — no equations.→ Interactive3D: the collapse seen from a particle and a random field fragment; the long read.→ ProgrammeProblem, methods, validation ladder, timeline, resources.→ ResultsThreshold maps, 3D comparisons, figures and tables.→ LogThe detailed computation log: every run, bug and fix.→ DocumentsProblem statement, plans, stage designs, reports, literature audits.→ CodeThe pbhgr, PBHVlasov, PBHCosmo and sphdiag libraries — sources and archives.→ DataOutput files of the 1D and 3D runs for checking and re-analysis.→

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