Are Primordial Black Holes Five-Dimensional in the Dark Dimension Scenario?

Why a micron-sized fifth dimension changes black holes

The Dark Dimension Scenario places the Standard Model on a brane inside a fifth dimension roughly a micron across, a corner of theory space that Swampland principles reach given the observed smallness of the cosmological constant and existing cosmological and tabletop constraints. In that setting, the question of whether a primordial black hole is four-dimensional or five-dimensional is not cosmetic: a five-dimensional black hole evaporates more slowly than its four-dimensional counterpart, which relaxes existing observational limits on black holes as dark matter.

The paper's answer is that the fifth dimension wins. Working through the standard production mechanisms, the authors conclude that, under mild assumptions and with quantum gravity constraints applied, primordial black holes must be five-dimensional regardless of their abundance. The qualifier that carries real weight is the escape hatch: a viable route would require exotic new physics at low energies.

The normalcy temperature separates two cosmic eras

Above a characteristic temperature called the normalcy temperature, the early universe behaves as a higher-dimensional system; below it, the universe is effectively four-dimensional with stabilized geometric moduli. In the Dark Dimension Scenario the normalcy temperature is about a GeV, a value fixed by requiring that Kaluza-Klein gravitons emitted by brane radiation not overproduce dark matter.

The paper uses this threshold to organize its argument. Black holes that form above it must be checked against five-dimensional physics, and the authors derive constraints on how the extra dimension evolved before the temperature fell to the GeV scale. A central result is that the universe could not have been radiation dominated in that earlier epoch: a radiation-dominated expansion would overproduce Kaluza-Klein gravitons, so the moduli must instead have evolved along a kination solution, the maximal-friction trajectory. Combined with the observational upper bound of roughly 10 e-folds on a kination era, this places the onset of such an era above about 10 TeV.

Phase-transition black holes end up five-dimensional

For black holes seeded by overdensities from a phase transition, the relevant comparison is between the horizon mass at formation and the Gregory-Laflamme threshold, the mass of a black hole whose size equals the extra dimension. Below that threshold a four-dimensional black hole is unstable and undergoes a Gregory-Laflamme transition into a five-dimensional structure.

Using the kination-era horizon mass, the paper finds that for any formation temperature above a TeV the mass sits far below the Gregory-Laflamme threshold. Keeping a primordial black hole four-dimensional would therefore require formation at or below roughly a TeV, which would demand a new, unknown phase transition in the Standard Model at sub-TeV scales, unlikely given how well the Standard Model is tested there. The authors also note that QCD confinement is a crossover rather than a first-order transition, so it is not an efficient generator of primordial black holes; relying on it would again require exotic low-energy physics.

The lifetime estimate sharpens the point. For a black hole formed at temperature T above the normalcy temperature, the lifetime scales as roughly 10^49 (GeV/T)^6 Planck times, so a lifetime shorter than the age of the universe requires formation above about 10^7 GeV, only about two orders of magnitude below the five-dimensional Planck scale of roughly 10^9 GeV. The authors therefore judge it far more likely that all five-dimensional black holes formed from phase transitions live longer than the current age of the universe.

Cosmic-string loops are born five-dimensional

Cosmic strings in this setting are topological defects associated with axion-like particles, with an energy scale bounded above by the higher-dimensional Planck scale. A black hole forms when a loop collapses to a size smaller than its Schwarzschild radius, and the loop size is limited by the Hubble radius.

Comparing the resulting mass bound with the Gregory-Laflamme threshold, the paper finds that a primordial black hole formed from cosmic-string collapse above a GeV must be five-dimensional: the condition for staying four-dimensional would require an extra dimension smaller than about 10^-6 microns, whereas the Dark Dimension Scenario has a micron-scale dimension. For formation below the normalcy temperature, the same comparison only allows four-dimensional black holes at temperatures below about 10 keV, too low for QCD axions and problematic for generic axion-like particles. Pushing the symmetry-breaking scale that low would make the axion-photon coupling parametrically large, in strong tension with laboratory, astrophysical, and cosmological bounds. The conclusion is unconditional: primordial black holes from cosmic-string collapse are always five-dimensional.

Long lifetimes open an observational handle

Because five-dimensional black holes evaporate more slowly, the paper examines whether some could survive to late times and evaporate now. It states that primordial black holes formed from cosmic strings can have lifetimes comparable to the age of the universe, which is what makes a late-time evaporation signal conceivable.

The authors connect this to the recent KM3NeT detection of a high-energy neutrino, whose energy is intriguingly close to the five-dimensional Planck scale in the Dark Dimension Scenario. They treat this as a potential connection rather than a demonstrated one, and they note that conclusions from earlier work on neutrinos from primordial black holes in extra-dimensional theories are expected to remain valid, supporting five-dimensional primordial black holes as a possible source of the observed event.

Two viable routes, one shared outcome

The paper's comparison across mechanisms is the part that matters for judging the claim. Inflation is excluded from the viable set not because it fails to make black holes but because its fine-tuned initial conditions and the scalar potential it requires are in tension with Swampland principles. That leaves early-universe phase transitions and axion-charged cosmic strings from symmetry breaking.

The two routes differ in how they arrive at the same endpoint. Phase-transition black holes can start as four-dimensional unstable objects and then evolve into five-dimensional structures through the Gregory-Laflamme instability, a conversion that depends on a kination era existing beyond the normalcy temperature. Cosmic-string loops, by contrast, are generated as five-dimensional structures whether production happens above or below the normalcy temperature. The authors also test the alternative where overproduction of radion-induced Kaluza-Klein modes drives the universe to critical density too quickly; in that case there is a negligible or nonexistent kination phase, primordial black holes form exclusively from collapsing cosmic strings, and they still emerge five-dimensional.

Where the five-dimensional claim holds and where it stops

The conclusion is conditional on the Dark Dimension Scenario itself, with its micron-scale fifth dimension and normalcy temperature near a GeV, and on the assumption that no additional extra dimensions exist beyond that fifth dimension. It also assumes no exotic new physics at low energies; a new sub-TeV phase transition, or a low-scale symmetry-breaking transition that produces the relevant strings, would be the kind of physics that could reopen the four-dimensional possibility, and the paper argues such options are disfavored rather than impossible.

Within those bounds, the paper's priority is a shift in how primordial black holes should be counted. The interesting split is not between abundant and rare black holes but between production histories: phase-transition black holes reach five dimensions through a Gregory-Laflamme conversion that hinges on a contingent kination era, while cosmic-string black holes are five-dimensional from birth under either cosmological history. That makes cosmic-string collapse the more robust route to five-dimensional primordial black holes, and it is the route whose lifetimes the authors flag as potentially comparable to the age of the universe.

Sources used in this answer