  In this article, we investigate the stochastic gravitational waves (GWs)
spectrum, resulting from the emission of gravitons through bremsstrahlung, in
the decay of particles produced by Hawking radiation. Although particle decays
inevitably entail the emission of graviton due to bremsstrahlung, the
associated decay width is notably suppressed due to the Planck scale
suppression in the coupling of matter fields to gravitons. Consequently, the
relic abundance of such GWs constituted of these gravitons undergoes a
corresponding reduction. However, we demonstrate that super-heavy particles,
reaching masses as high as Planck scale, can emerge naturally in the Hawking
radiation of evaporating primordial black holes (PBHs) and can compensate for
this suppression. In addition, we also discuss the stochastic gravitational
waves constituted out of the gravitons directly radiated from such evaporating
PBHs. When the super-heavy particle decays promptly after its production, then
the corresponding GW spectrum remains subdominant to the one arising from
direct PBH evaporation. However, if this particle is long-lived and decays
after PBH evaporation, then the resulting GWs produced in these two processes
have two distinct spectra with their peaks at extremely high frequencies,
providing avenues for proposed ultra-high frequency gravitational wave
detectors. We also show that such gravitational waves contribute significantly
to substantial dark radiation, which can be probed with the enhanced
sensitivity of future experiments.
