Primordial black hole constraints with Hawking radiation -- a review

Primordial black holes are under intense scrutiny since the detection of gravitational waves from mergers of solar-mass black holes in 2015. More recently, the development of numerical tools and the precision observational data have rekindled the effort to constrain the black hole abundance in the lower mass range, that is $M < 10^{23}$g. In particular, primordial black holes of asteroid mass $M \sim 10^{17}-10^{23}\,$g may represent 100\% of dark matter. While the microlensing and stellar disruption constraints on their abundance have been relieved, Hawking radiation of these black holes seems to be the only detection (and constraining) mean. Hawking radiation constraints on primordial black holes date back to the first papers by Hawking. Black holes evaporating in the early universe may have generated the baryon asymmetry, modified big bang nucleosynthesis, distorted the cosmic microwave background, or produced cosmological backgrounds of stable particles such as photons and neutrinos. At the end of their lifetime, exploding primordial black holes would produce high energy cosmic rays that would provide invaluable access to the physics at energies up to the Planck scale. In this review, we describe the main principles of Hawking radiation, which lie at the border of general relativity, quantum mechanics and statistical physics. We then present an up-to-date status of the different constraints on primordial black holes that rely on the evaporation phenomenon, and give, where relevant, prospects for future work. In particular, non-standard black holes and emission of beyond the Standard Model degrees of freedom is currently a hot subject.