New models of nonsingular black hole dark matter from limiting curvature

TL;DR

This work investigates nonsingular black holes that obey a limiting-curvature condition as candidates for primordial black hole dark matter. By introducing a mass-dependent regulator through $L^3 = 2 G M \ell^2 f(\hat{\ell})$ with $\hat{\ell} = \ell/(2GM)$, the authors study both de Sitter and Minkowski core models, revealing horizon-scale modifications and new black hole mass bands where horizons exist. They derive thermodynamic properties, identify band-edge behavior with vanishing Hawking temperature and heat capacity, and estimate lifetimes using a Stefan–Boltzmann approach, finding negligible mass loss for $M \gtrsim 10^{15}$ g. They then constrain the PBH dark matter fraction from extragalactic gamma-ray background observations, showing that these models can accommodate a substantial $f_{\text{pbh}}$ compared to the Schwarzschild case. Collectively, the results demonstrate that limiting-curvature nonsingular PBHs with regulator-scale effects can viably contribute to dark matter and motivate future UV-complete theories that yield such metrics.

Abstract

We consider phenomenological models for nonsingular black holes that satisfy the limiting curvature condition (i.e., that have curvatures that are always sub-Planckian in size) while having a more general dependence on the black hole mass than the most studied examples. These models allow black holes to exist while having regulators that are larger than the horizon scale; it has been shown previously that this can lead to observable consequences in an astrophysical setting, for allowed choices for the regulator scale. Noting that substantial horizon-scale modifications of the metric will affect black hole thermodynamics and Hawking radiation, we study these metrics in the context of primordial black hole dark matter. Considering examples with de\,Sitter and Minkowski cores, respectively, we study the effect of the regulator in these metrics on the allowed black hole mass ranges (or ``bands"), the black hole temperature, specific heat and lifetime, and the bounds on the primordial black hole fraction of the total dark matter density from the observed extragalactic gamma ray background.

Figures (7)

• Figure 1: Horizon structure in the de Sitter core example. The shaded regions correspond to parameter choices for which horizons exist.
• Figure 2: Horizon structure in the Minkowski core example. The shaded regions correspond to parameter choices for which horizons exist.
• Figure 3: For $\epsilon=0$, we visualize the Hawking temperature normalized to the Schwarzschild value (solid line) as well as the specific heat normalized to the absolute Schwarzschild value (dashed line) as a function of the dimensionless mass parameter $\mu = GM/\ell$. The left panel shows the de Sitter core case, and the right panel shows the Minkowski core case. The black hole band structure is highlighted as a solid bar in the upper part of each panel. For masses outside this region, displayed in light gray, no black holes exist. This figure is shown as a point of comparison as the limiting curvature condition requires $\epsilon$ to be nonzero.
• Figure 4: For $\epsilon=0.001$, we visualize the Hawking temperature and specific heat normalized for the de Sitter core case (left) and the Minkowski core case (right) in an identical fashion to Fig. \ref{['fig:thermo-epsilon=0']}. The non-trivial band structure induced by $\epsilon > 0$ is visualized via a zoomed-in view in the second row, highlighting the existence of a mass gap in the lower black hole band. In both cases, the qualitative behavior of the Hawking temperature and specific heat is identical to the behavior at the lower end of the second part of the black hole band spectrum.
• Figure 5: Given a choice of initial regulator $\hat{\ell}_0= \ell/(2GM_0)$ and black hole model, we plot the evolution of the normalized black hole mass as a function of dimensionless time (measured in the age of the Universe $t_0$). The left panel shows the case of de Sitter core black holes with $\hat{\ell}_0 = 4$ and $\epsilon=0.001$, and the right panel depicts the case of the Minkowski core black holes with $\hat{\ell}_0 = 2$ and $\epsilon=0.001$. For the masses greater than approximately $10^{15}$ g, which are considered throughout the rest of this paper, the black hole mass loss is hence small enough that their masses may be considered constant over the lifetime of the Universe.