5D Rotating Black Holes as dark matter in Dark Dimension Scenario: Hawking Radiation versus the Memory Burden Effect

This work explores the possibility that five-dimensional primordial rotating black holes could account for all, or a significant portion, of the dark matter in our universe. Our analysis is performed within the context of the ``dark dimension’’ scenario, a theoretical consequence of the Swampland Program that predicts a single micron-scale extra dimension to explain the observed value of dark energy. We demonstrate that within this scenario, the mass loss of a primordial rotating black hole sensitive to the fifth dimension is significantly slower than that of its four-dimensional counterpart. Consequently, primordial black holes with an initial mass of $M\gtrsim 10^{10}$g can survive to the present day and potentially constitute the dominant form of dark matter. Finally, we investigate the memory burden effect and find that it dramatically prolongs the lifetime of five-dimensional rotating primordial black holes, making them compelling candidates for all the dark matter in the universe.

💡 Research Summary

The paper investigates whether five‑dimensional (5D) rotating primordial black holes (PBHs) can constitute the dark matter of the Universe within the “dark dimension” scenario, a Swampland‑motivated framework that predicts a single extra dimension of micron‑scale size. The authors first review the Swampland Distance Conjecture and its implication that the observed tiny cosmological constant Λ forces a Kaluza‑Klein (KK) tower with a mass scale m_KK ≈ |Λ|^{1/4} ≈ 6 meV, corresponding to an extra‑dimensional radius R_C ≈ 1 µm. The associated 5D Planck scale is M_* ≈ 10¹⁰ GeV, setting the fundamental scale for black‑hole physics in this model.

In a regime where the black‑hole horizon radius r_S satisfies ℓ_s ≪ r_S ≪ R_C (ℓ_s is the string length), gravity propagates in five dimensions and the metric reduces to the higher‑dimensional Schwarzschild–Tangherlini solution. The Hawking temperature then scales as T_BH = (n+1)/(4πr_S) with n = 1, i.e. T_BH ∝ 1/r_S, which is lower than in four dimensions for the same mass. Consequently, the power radiated by a 5D black hole scales as P ∝ T^{n+4} r^{n+2} ∝ T³ r³, leading to a dramatically suppressed evaporation rate compared with the 4D case.

The authors extend previous work on non‑rotating PBHs to the rotating Myers‑Perry black holes in five dimensions. They solve the coupled evolution equations for mass M and angular momentum J, using grey‑body factors appropriate for brane‑localized Standard Model fields (the dominant emission channel). Their analysis shows that the spin‑down phase lasts of order 10⁹ years, during which the black hole loses roughly 40–60 % of its mass. After the spin vanishes, the remnant behaves as a non‑rotating 5D Schwarzschild black hole whose lifetime, computed from the suppressed Hawking power, is also of order 10⁹ years. Putting the two phases together yields a total lifetime τ_total ≈ (1–2) × 10⁹ yr for an initial mass M₀ ≈ 10¹⁰ g. Thus, PBHs with M₀ ≳ 10¹⁰ g can survive to the present epoch, far below the usual 4D bound of ≈ 5 × 10¹⁴ g.

A novel ingredient is the “memory burden” effect proposed by Dvali. As a black hole evaporates, it retains quantum information from absorbed matter, building up an informational load that feeds back on the evaporation rate. The authors model this by modifying the emission rate with a factor (1 + M/M_c)^{-α}, where M_c ≈ 10⁹ g and α ≈ 1. This suppression further lengthens the lifetime by a factor of 2–3, allowing even lighter PBHs (down to ∼10¹⁰ g) to persist today.

The paper also surveys observational constraints. Laboratory tests of Newton’s law down to ∼30 µm restrict the extra dimension to ≤ 1 µm, consistent with the dark‑dimension hypothesis. Gamma‑ray, CMB, and microlensing bounds that exclude 4D PBHs in the mass range 10¹⁵–10¹⁷ g are relaxed because the suppressed Hawking emission reduces the associated high‑energy particle fluxes. Consequently, the allowed parameter space for 5D rotating PBHs is considerably larger.

Finally, the authors estimate the required PBH formation fraction f_PBH to account for the observed dark‑matter density Ω_DM. Assuming a broad initial mass spectrum peaked around 10¹⁰ g and a formation efficiency f ≈ 10⁻²–10⁻¹, the total PBH density can saturate Ω_DM. This demonstrates that, within the dark‑dimension framework, rotating 5D PBHs—especially when the memory‑burden effect is included—are viable dark‑matter candidates, opening a new avenue for connecting Swampland conjectures, extra‑dimensional gravity, and cosmological observations.