5D Rotating Black Holes as dark matter in Dark Dimension Scenario: Hawking Radiation versus the Memory Burden Effect (2512.10381v1)

Abstract: 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.

• The paper demonstrates that 5D rotating PBHs exhibit extended lifetimes due to higher-dimensional Hawking suppression and the memory burden effect.
• It employs a detailed semi-analytical calculation of greybody factors and evolution equations to quantify the spin-down and mass-loss dynamics.
• The study establishes a viable dark matter candidate by reconciling Swampland-inspired extra dimensions with quantum black hole microphysics.

Five-Dimensional Rotating Black Holes as Dark Matter in the Dark Dimension Scenario

Theoretical Framework: Swampland Program and the Dark Dimension Scenario

The paper analyzes the possibility that five-dimensional (5D) rotating primordial black holes (PBHs) constitute all, or a significant fraction, of dark matter under the "dark dimension" scenario—an extension inspired by Swampland Program conjectures that posit a single, micron-scale extra spatial dimension. The Swampland constraints, particularly the Distance Conjecture and Weak Gravity Conjecture, are leveraged to motivate the existence of this extra dimension, whose Kaluza-Klein (KK) mass scale is set by the observed value of the cosmological constant, predicting a compactification radius of order $\mu$m.

In this construction, the Standard Model is realized on a D-brane transverse to the extra dimension, while gravity propagates in the bulk. The analysis focuses on the parametric sensitivity of the gravitational sector to extra-dimensional physics, with strong bounds imposed by tests of Newton’s law, spin-2 KK modes, and cosmological/astrophysical constraints. The species scale is derived to be $M_*\sim 10^{10}$ GeV—with KK masses above 6.6 meV—constraining the allowed black hole dynamics.

Higher-Dimensional PBH Phenomenology

Within this extra-dimensional framework, PBHs are theorized to emerge from enhanced small-scale primordial curvature perturbations, following inflaton decay and entering the Hubble horizon with a wide range of masses and non-zero (sometimes maximal) initial angular momenta. The paper precisely outlines the relationship between curvature power spectrum properties and PBH mass function.

Crucially, black hole metrics differ significantly at $r\ll R_C$ versus $r \gg R_C$, exhibiting higher-dimensional geometry in the former regime which impacts their thermodynamics and evaporation. For 5D Schwarzschild-Tangherlini black holes, the Hawking temperature and entropy scale differently with mass than in 4D—directly affecting evaporation timescales.

The semiclassical Hawking evaporation rate is computed with brane-localized Standard Model fields dominating the emission. The dimensional enhancement to the event horizon size in five dimensions leads to substantial suppression of the Hawking temperature and radiation rate, thus extending PBH lifetimes dramatically. Numerically, with $M_*\sim 10^{10}$ GeV, PBHs with initial mass $M_{\text{PBH}}\gtrsim 10^{11}$ g are found to survive until the present, opening the window for PBHs to constitute cosmological dark matter, in sharp contrast to the 4D case where $M_{\text{PBH}}\gtrsim 5\times 10^{14}$ g are required.

Rotating 5D Black Holes: Dynamics and Evaporation

The core technical contribution is the detailed calculation of the mass and angular momentum evolution for 5D rotating PBHs (Myers–Perry black holes with one nonvanishing spin parameter). The precise structure of the horizon, temperature, and angular momenta in the context of higher dimensions is employed, with the event horizon shrinking as rotation increases, leading to lower Hawking temperatures.

The authors compute the greybody factors semi-analytically in a low-frequency expansion for brane-localized emission, allowing a credible estimate of the Hawking spectra for arbitrary particle species and spins. The coupled evolution equations for mass and angular momentum loss are solved, yielding an analytical $M(J)$ relation that governs the black hole’s decay trajectory, and the time evolution is fully described through explicit integration.

A significant result is the finding that, for typical initial angular momenta, 5D rotating PBHs lose between 40–60% of their initial mass in the spin-down phase, which lasts $\mathcal{O}(10^9)$ years for $M_{\text{PBH}}\sim 10^{12}$ g. The post–spin-down Schwarzschild regime contributes an additional $\mathcal{O}(10^8)$ year lifetime, but this is subdominant for the range of parameters considered. This lifespan is a direct consequence of the suppressed Hawking radiation in 5D, reinforcing that much lighter PBHs than in the 4D case can constitute dark matter.

The calculations are quantitatively sensitive to the accurately estimated greybody factors, with variations in the spin parameter $a_*$ and the mass/rotation loss-rate ratios (denoted $\eta$) carefully analyzed. Above-threshold angular momentum ($a_*>\sqrt{\mu}$) is forbidden, and the maximal allowed values are respected throughout.

The Memory Burden Effect and Extended PBH Longevity

The paper incorporates the "memory burden effect," wherein black holes, as they evaporate, accumulate a quantum informational load from their initial state, which subsequently suppresses the evaporation rate. The Hamiltonian model introduced captures the evolution of this memory-induced stabilization, with the entropy-dependent suppression factor $1/S^p$ modulating the mass-loss rate. Depending on the exponent $p$, the onset of evaporation suppression occurs either almost instantaneously or after a critical fraction of the initial mass is lost.

The theoretical implications are profound: for $p\gtrsim 2$, the memory burden effect dramatically extends black hole lifetimes, stabilizing PBHs with $M\lesssim 10^{10}$ g that would otherwise have evanesced via Hawking emission. This stabilization mechanism removes the lower bound on dark-matter–viable PBH masses, allowing a wider PBH mass function—including those that would violate Big Bang Nucleosynthesis bounds in the standard scenario—to survive and contribute to or even dominate the dark matter density today.

Tabulated results show for standard Hawking evaporation ($p=0$), $\tau\propto M^2$; for $p=1$ (instantaneous memory burden), $\tau \propto M^{7/2}$; and for $p=2$, $\tau\propto M^5$, yielding extended PBH stability at astrophysical scales.

Implications and Future Directions

The main theoretical implication of this work is the confluence of Swampland-inspired extra-dimensional models with black hole quantum microphysics leading to a dynamically extended window for PBH dark matter. The combined suppression from higher-dimensional Hawking radiation and the quantum memory burden effect robustly allows PBHs with $M\gtrsim 10^{10}$ g to survive for a Hubble time, substantially widening the parameter space for PBH dark matter.

Practically, the results indicate that PBHs in the 5D dark dimension scenario with initial masses well below the 4D evaporation threshold are viable dark matter candidates, unconstrained by traditional CMB or galactic background bounds. The memory burden effect, if ultimately confirmed as a generic property of quantum black holes, implies the existence of stable or superlong-lived sublunar-mass black holes. This brings unique observational signals, such as delayed or suppressed signals from Hawking-emitted particles, which can be targeted in future cosmic-ray, gamma-ray, or 21-cm measurements.

Theoretically, the findings motivate a deeper investigation of quantum aspects of black hole information storage and loss in the presence of extra dimensions, and their cosmological consequences. They also suggest new model-building directions for the Swampland Program, ensuring self-consistency in low-energy EFTs with light KK mode towers and mini black holes.

Future work should include a more complete calculation of greybody factors beyond the low-frequency regime, incorporation of bulk graviton emission, and a systematic population synthesis of PBHs formed during inflationary reheating, with full accounting for their angular momentum distribution and the corresponding memory burden effect as a function of cosmic time.

Conclusion

The paper establishes that 5D rotating PBHs, arising naturally in Swampland-motivated dark dimension models, experience a Hawking evaporation suppression sufficient for their survival as viable dark matter constituents. Incorporation of the memory burden effect further extends their lifetimes, making PBHs with masses well below conventional lower bounds compelling candidates for the cosmic dark matter. This line of inquiry reframes the cosmological role of PBHs within extra-dimensional, quantum information–driven frameworks, suggesting rich observational and phenomenological consequences for future studies.