Value of the entropy-suppression exponent k in memory-burden evaporation

Determine the numerical value of the exponent k that governs the entropy-suppressed emission rate dN_mb/(dE dt) = S^{-k} dN_sc/(dE dt) during the memory-burden phase of black hole evaporation. Pinning down k is required to predict black-hole lifetimes, particle-emission rates, and the resulting dark-matter phase-space distributions.

Background

In the memory-burden framework, the semi-classical emission rate is argued to be suppressed by a power of the Bekenstein–Hawking entropy, S^{-k}. The exponent k controls how drastically evaporation slows and thereby impacts cosmological constraints and viable parameter space for non-cold dark matter produced by primordial black holes.

While estimates have suggested k in the range 1–3, its exact value remains undetermined, leading the authors to treat k as a free parameter and explore its phenomenological consequences.