Primordial regular black holes as all the dark matter. I. Time-radial-symmetric metrics

Primordial black holes (PBHs) are usually assumed to be described by the Schwarzschild or Kerr metrics, which however feature unwelcome singularities. We study the possibility that PBHs are non-singular objects, considering three phenomenological, regular tr (time-radial)-symmetric space-times (including the well-known Bardeen and Hayward ones), featuring either de Sitter or Minkowski cores. We characterize the evaporation of these PBHs and constrain their abundance from $\gamma$-ray observations. For all three metrics we find that constraints on $f_{\text{pbh}}$, the fraction of dark matter (DM) in the form of PBHs, weaken with respect to the Schwarzschild limits, because of modifications to the PBH temperature and greybody factors. This moves the lower edge of the asteroid mass window down by potentially an order of magnitude or more, leading to a much larger region of parameter space where PBHs can make up all the DM. A companion paper is devoted to non-\textit{tr}-symmetric metrics, including loop quantum gravity-inspired ones. Our work provides a proof-of-principle for the interface between the DM and singularity problems being a promising arena with a rich phenomenology.