Quantum Oppenheimer-Snyder primordial black holes as all the dark matter

Abstract

Primordial black holes (PBHs) are widely considered as candidates for dark matter in many recent studies, and they are often modeled as Schwarzschild or Kerr black holes (BHs), which have curvature singularities. Nevertheless, resolving the classical singularity may require quantum gravity motivated corrections, thereby yielding an effective quantum corrected BH spacetime geometry different from the Schwarzschild or Kerr cases. Therefore, it is well motivated to consider BHs beyond the Schwarzschild or Kerr as viable PBH candidates. Based on these considerations, we investigate quantum Oppenheimer Snyder BHs as PBHs which could account for all the dark matter. Our results show that these BHs have temperatures and greybody factors markedly different from the Schwarzschild case, suppressing Hawking emission and thereby relaxing the $γ$-ray constraints from HEAO-1, COMPTEL, and EGRET, which, relative to the Schwarzschild case, broadens the allowed PBH mass window in the asteroid-mass range where PBHs can constitute all of the dark matter.

Figures (4)

• Figure 1: Normalized BH temperature $T/T_{\rm Sch}$ versus $\alpha/r_H^{2}$. Here $T$ is the temperature of the qOS BH and $T_{\rm Sch}$ is the temperature of the Schwarzschild BH. For convenience, we set $M=1$ in this figure.
• Figure 2: Greybody factors are shown as a function of $\omega r_H$. In this plot, we set $s=1$ and $l=1$. Moreover, the solid purple line corresponds to the Schwarzschild case, while the dashed, dotted, and dot-dashed blue lines correspond to qOS BHs with $\alpha=0.3r_{H}^2$, $\alpha=0.45r_{H}^2$, and $\alpha=0.6r_{H}^2$, respectively.
• Figure 3: The particle number density of the Hawking radiation as a function of particle energy. We fix the mass of PBH $M_{pbh}=10^{16}\,\mathrm{g}$ and show the results. The solid line is the Schwarzschild case, the dashed line is the qOS case for $\alpha=0.3r_{H}^{2}$, the dotted line is the qOS case for $\alpha=0.45r_{H}^{2}$ and the dotted dashed line is the qOS case for $\alpha=0.6r_{H}^{2}$.
• Figure 4: The dark-matter fraction of PBHs as a function of PBH mass. The solid line corresponds to the Schwarzschild case. The dashed, dotted, and dot-dashed lines correspond to qOS PBHs with different values of $\alpha$, respectively.