Secondary gravitational wave signatures from 5D rotating primordial black holes in the dark dimension

We investigate five-dimensional rotating primordial black holes (PBHs) as dark matter candidates within the dark dimension scenario motivated by the Swampland Program. In this framework, a micron-scale extra dimension modifies Hawking evaporation, while a phenomenological memory-burden factor S − p can further prolong PBH lifetimes. We compute the evaporation dynamics for rotating 5D PBHs, derive the burdened lifetime scaling, and study the fiducial p = 2 benchmark over 10 10 g ≲ M ≲ 10 21 g . The curvature perturbations responsible for PBH formation also generate a stochastic gravitational wave background through second-order scalar-induced effects. Assuming a log-normal primordial power spectrum with σ = 1 and f PBH = 1 , we calculate the present-day energy density Ω GW h 2 across this benchmark interval. The predicted signals peak at frequencies from nHz to Hz, within the sensitivity ranges of LISA and DECIGO/BBO. Fisher forecasts illustrate the prospective sensitivity to the PBH mass, dark matter fraction, spectral width, and phenomenological exponent p . A joint test of the gravitational-wave spectrum and the evaporation history could probe extradimensional PBHs and memory-burden phenomenology.