Chapter 06 · Black Holes/Hawking Radiation

Primordial Black Hole Evaporation

1974 · Bernard Carr, Stephen Hawking, Anne Green, Bradley Kavanagh, Florian Kuhnel

If the early universe produced light enough black holes, Hawking radiation would have evaporated them by now or be evaporating them today. Heavier primordial black holes could be some or all of dark matter. Fifty years of searches and no confirmed detection.

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In one sentence

If the early universe produced black holes lighter than about 10^11 kilograms, Hawking radiation would have evaporated them by now or be evaporating them today, possibly producing observable gamma-ray bursts, neutrinos, or gravitational waves. Heavier primordial black holes would still exist and could account for some or all of dark matter. Carr and Hawking proposed this in 1974; fifty years of searches have set tight upper limits without a confirmed detection.

The claim

Carr and Hawking's 1974 paper combined two ideas. First, the very early universe could have produced black holes through density fluctuations: any patch dense enough to overcome its own expansion pressure would collapse to a black hole. Second, Hawking's just-derived evaporation result meant these primordial black holes (PBHs) would have lifetimes set by their mass. Specifically, a PBH of mass M evaporates in time roughly proportional to M cubed, so PBHs around 10^11 kilograms (a hundred-million-billion grams) would be evaporating now. Their final-stage radiation would produce a characteristic gamma-ray burst signature, detectable in principle. Heavier PBHs would still exist today and could be a dark matter candidate; lighter ones already evaporated, possibly leaving an early-universe particle-physics signature.

The dark matter framing took over in the 2010s. LIGO's 2015 detection of merging black holes of about 30 solar masses raised the question of whether some of these could be primordial. If so, PBHs in the 1 to 100 solar mass range could comprise a fraction of dark matter, possibly all of it. The PBH-as-dark-matter scenario has the appeal that it requires no new particle physics, only well-understood quantum gravity (Hawking radiation) and well-understood cosmology (early-universe perturbations). The 2010-2025 PBH literature has consolidated observational constraints: microlensing surveys (EROS, MACHO, OGLE, Subaru-HSC) bound the stellar-mass range, gamma-ray missions bound the evaporating-now range (about 10^11 kg), CMB spectral distortions and cosmological backreaction bound the supermassive end. The Carr-Kuhnel-Sandstad 2016 review and the Green-Kavanagh 2021 review consolidate the current constraints.

After 50 years of searches, no PBH evaporation signature has been confirmed. The Fermi gamma-ray telescope and other detectors have set increasingly tight upper limits on the local PBH density in the evaporating-now mass range. The window for PBHs comprising all of dark matter has narrowed substantially since 2015, with surviving allowed mass ranges concentrated around the asteroid-mass scale (10^17 to 10^23 kg). The NANOGrav 2023 pulsar-timing-array detection of a gravitational-wave background has reopened questions about whether some signal could be consistent with a PBH-merger population. The PBH-as-dark-matter scenario is neither confirmed nor ruled out; the active questions are whether tightening constraints will close the surviving windows or whether some new observational channel will produce a positive signal.

The family stance

Black holes are not black. Hawking's 1974 derivation showed they emit thermal radiation at a temperature set inversely by their mass, and that they have entropy proportional to their horizon area. Every candidate theory of quantum gravity reproduces this leading-order result. The completeness questions, what happens to the radiation past the Page time (unitarity), what the radiation does to the geometry it leaves behind (backreaction), and what cuts off the high-energy modes near the horizon (trans-Planckian), have been substantially clarified since 2019 but are not fully closed. Direct astrophysical observation is theoretically possible but practically inaccessible with current and foreseeable instruments.

Predictions

Primordial black holes of mass about 10^11 kilograms (about 10^14 grams) should be evaporating now and producing detectable gamma-ray bursts in the GeV range; the predicted spectrum and event rate are calculable from the Hawking formula
Heavier primordial black holes (10^17 to 10^23 kilograms, asteroid-mass) could comprise all of dark matter without violating current observational constraints; specific microlensing and CMB signatures should appear if the abundance is high enough
PBH mergers should contribute to LIGO/Virgo gravitational-wave signals if PBHs are a significant fraction of dark matter in the stellar-mass range; the predicted mass distribution, spin distribution, and event rate would differ from astrophysical black hole mergers
The NANOGrav 2023 pulsar-timing-array gravitational-wave background could be partly consistent with a primordial-black-hole merger population at solar-mass scales; this remains an active research question

Evidence

Carr-Hawking 1974 established the theoretical framework: density fluctuations in the early universe can produce black holes, and Hawking's evaporation formula determines their lifetimes; the framework is universally accepted
Carr-Kuhnel-Sandstad 2016 consolidated observational constraints across the full PBH mass range, providing the canonical reference for which mass windows are still allowed as dark matter candidates
Green-Kavanagh 2021 updated the constraint picture through the LIGO era, refining bounds and surfacing the surviving allowed windows
The framework requires no new particle physics, only well-understood quantum gravity and well-understood early-universe cosmology; this is a non-trivial parsimony argument compared to particle dark matter candidates

Counterpoints

No PBH evaporation signature has been detected despite 50 years of searches. Fermi, INTEGRAL, EGRET, and other gamma-ray missions have set upper limits in the evaporating-now mass range; no positive detection has been confirmed
Observational constraints are tight across most mass ranges. The surviving windows for PBHs comprising all of dark matter are narrow, concentrated around the asteroid-mass scale (10^17 to 10^23 kg); broader mass distributions are more easily ruled out than monochromatic populations
LIGO/Virgo black hole mergers are statistically consistent with astrophysical (non-primordial) origin; PBH contributions remain a research question rather than a confirmed signal
The PBH-as-all-dark-matter scenario requires specific early-universe physics (large enhanced perturbations at small scales) that has not been independently observed; the mechanism is not ruled out but is not directly evidenced either

Variants in this family

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▸Go deeperTechnical detail with proper terminology

PBH formation: primordial black holes form when a Hubble-volume-scale density perturbation exceeds about 30% of the critical density, allowing the patch to collapse against its own expansion. The required perturbation amplitude is much larger than the about 10^-5 amplitude observed in the CMB at large scales; PBH-forming small-scale perturbations would require enhancement during inflation (peaks in the power spectrum at the relevant scale).

Evaporation timescale: the lifetime of a Schwarzschild black hole of mass M is approximately t_evap = (5120 pi G^2 M^3) / (hbar c^4). Plugging in numbers: solar-mass BH lives about 10^67 years; a 10^11 kg PBH lives about 10^10 years (about the current age of the universe); a 10^9 kg PBH lives about 10^4 years (long evaporated).

Mass-range constraints (Green-Kavanagh 2021 summary): below 10^14 g, PBHs have evaporated already; about 10^14 g, evaporation signatures excluded by gamma-ray bounds; 10^17 to 10^23 kg (asteroid mass), open window with surviving allowed regions; 10^23 to 10^25 kg (lunar mass), microlensing bounds; about 1 to 100 solar masses, LIGO bounds; above this, CMB distortion bounds.

NANOGrav 2023 implications: the pulsar-timing-array gravitational-wave background signal at nanohertz frequencies is most naturally explained by supermassive black hole binary mergers, but alternative interpretations include cosmic-string networks and primordial-black-hole-merger populations. The PBH interpretation requires specific PBH mass distributions that produce the right amplitude and spectral shape; current evidence is inconclusive.