Dark matter production from evaporation of regular primordial black holes

TL;DR

The paper shows that keeping the dimensionless regularization parameter $l = L/(GM)$ fixed enables self-similar, complete evaporation of regular primordial black holes (RPBHs) and avoids remnants, while preserving key Hawking-like scaling. It develops a general analytic framework to compute dark matter production from RPBH evaporation, applying it to Hayward and Simpson-Visser metrics, and derives how the DM abundance depends on the RPBH initial mass, formation fraction, and metric parameters. Cosmological constraints from inflation, BBN, and warm DM are translated into bounds on the RPBH parameter space, revealing shifts relative to the standard Schwarzschild PBH case. The work provides ready-to-use formulas and highlights that observational probes, including gravitational waves, could discriminate between regular and singular black holes via their evaporation products and formation histories.

Abstract

We point out that a simple redefinition of the regularizing parameter in regular black hole (RBH) metrics can preserve the self-similarity of the evaporation process. This implies that a RBH can evaporate completely, mirroring the behavior of its singular counterpart. Consequently, RBHs need not evolve into exotic, unverified remnant states such as horizonless compact objects or wormholes. We then provide a generic framework to study dark matter (DM) production from evaporation of regular primordial black holes (RPBHs). As illustrative examples, we explicitly work out the cases of the Hayward metric and the Simpson-Visser metric. The formalism can be readily applied to other metrics. RPBH generally exhibits different Hawking temperature and horizon size compared to their singular counterpart, leading to distinct lifetime and mass evolution. We calculate the resulting modified cosmological constraints and the allowed parameter space to obtain the correct DM abundance. This intriguing scenario provides a unified resolution to both the DM problem and the black hole singularity problem, while preserving the standard self-similar evaporation process.

Figures (5)

• Figure 1: Schematic sketch comparing Hawking temperature of singular Schwarzschild BH with self-similar and non-self-similar types of regular BH.
• Figure 2: Upper left: Hawking temperature of RBH normalized to the Schwarzschild temperature as a function of regularizing parameter $l$. Upper right: Outer horizon radius of RBH normalized to Schwarzschild radius. Lower left: Lifetime of RBH normalized to lifetime of Schwarzschild black hole. Lower right: Mass evolution of a 1 g black hole with the regularizing parameters chosen to be close to the extremal values.
• Figure 3:
• Figure 4: Warm DM constraint on RPBH mass as a function of DM mass for different chosen values of $l$.
• Figure 5: In the left panel, the solid colored contours show the parameters that can obtain the correct DM abundance for the singular Schwarzschild PBH with different DM masses. The solid black line indicates $\beta=\beta_c$ above which there is PBH domination. The dashed colored and black contours are for the regular Hayward metric with $l=0.769$. The vertical dot-dashed gray line is inflation constraint for both PBH and RPBH. The vertical dot-dashed yellow line is BBN constraint for PBH, while the dotted yellow line is for RPBH. The faded portions of (solid or dashed) colored contours, if any, do not satisfy warm DM constraint. In the right panel, the same but for Simpson-Visser metric with $l=1.99$.