On extremal black holes

TL;DR

The paper investigates whether extremal black holes can exist in realistic, non-supersymmetric settings by incorporating environmental and quantum effects. For electrically charged extremal black holes, it shows that Schwinger discharge and ambient ionization impose stringent mass bounds, with a robust lower limit around $M \gtrsim 4.5\times 10^{14} M_\odot$, effectively ruling out astrophysical extremality. For magnetically charged cases, a Lee–Nair–Weinberg instability requires unrealistically large monopole charges for stability, and inflationary nucleation remains negligibly probable, further discouraging extremality. The work also discusses potential Kerr extremality loss via superradiant interactions with the stochastic gravitational-wave background, reinforcing the view that extremal black holes are unlikely to persist, though near-extremal rotating black holes may still provide valuable windows into quantum-gravity effects.

Abstract

We take a fresh look at the viability of physically realistic extremal black holes within our (non-supersymmetric) low energy physics. By incorporating prefactors and volume effects, we show that Schwinger discharge in charge neutral environments is far more efficient than commonly assumed. Using ionization estimates for neutral hydrogen, we obtain a new and robust lower bound on the mass of an extremal electrically charged black hole, exceeding $10^{14} M_\odot$. For magnetic black holes, we compute the Lee-Nair-Weinberg instability and revisit early universe pair creation rates, including singular instantons that substantially enhance production, to demonstrate that the extreme charges required for stability are cosmologically implausible. Finally, we suggest that an extremal Kerr black hole could shed angular momentum via superradiant scattering from the stochastic gravitational wave background. Taken together, our results provide a unified picture that extremal black holes of any type are unlikely to persist in our universe.

Figures (1)

• Figure 1: Instability of magnetically charged black holes. Plot of $\Omega$ for a magnetically charged black hole as a function of its mass $M$, expressed in units of the fundamental magnetic charge. For reasons of dynamic range we only display results for low $N$. Each curve corresponds to a different winding number $N$, as indicated in the legend. The black dots mark the extremal limit: the minimum mass possible for a black hole with the given charge. Accordingly, the curves do not extend beyond this point. We adopt natural units with $G=c=\hbar=4\pi\epsilon_0=1$, and set $\eta=10^{-4}$ and $g=1$, so that the fundamental magnetic charge is unity and the charge of the black hole is $Q=N$. The mass of the extremal black hole equals $N$.