Swampland Statistics for Black Holes

In this work, we approach certain black hole issues, including remnants, by providing a statistical description based on the weak gravity conjecture in the swampland program. Inspired by the Pauli exclusion principle in the context of the Fermi sphere, we derive an inequality which can be exploited to verify the instability manifestation of non-supersymmetric four dimensional black holes via a characteristic function. For several species, we show that this function is in agreement with the weak gravity swampland conjecture. Then, we deal with the cutoff issue as an interval estimation problem by putting an upper bound on the black hole mass scale matching with certain results reported in the literature. Using the developed formalism for the proposed instability scenarios, we provide a suppression mechanism to the remnant production rate. Furthermore, we reconsider the stability study of the Reissner-Nordstrom black holes. Among others, we show that the proposed instabilities prohibit naked singularity behaviors

💡 Research Summary

The paper under review attempts to connect the Weak Gravity Conjecture (WGC), a central element of the Swampland program, with the physics of four‑dimensional, non‑supersymmetric black holes. The authors introduce a statistical framework inspired by the Pauli exclusion principle and the concept of a Fermi sphere. By treating the black‑hole horizon as a two‑dimensional surface (S²) and the momentum space of particles on that surface as another two‑dimensional space (R²), they define a phase‑space volume S² × R². Within this phase space they count the number of accessible charged states, denoted z, using the standard quantum‑mechanical phase‑space measure (dx dp/ℏ²). This counting leads to a relation between z, the black‑hole mass M, the Hawking temperature T, and the gauge coupling g (or the unit charge‑to‑mass ratio of the constituent species).

From this counting they construct an “energy” associated with an asymmetric instability, E ∝ ℏ² z²/(G² M² m_g), where m_g is the mass of a unit‑charge particle. They then define a characteristic function ρ = Z⁻¹ exp