Electron-Positron Jets from a Critically Magnetized Black Hole

The curved spacetime surrounding a rotating black hole dramatically alters the structure of nearby electromagnetic fields. The Wald field which is an asymptotically uniform magnetic field aligned with the angular momentum of the hole provides a convenient starting point to analyze the effects of radiative corrections on electrodynamics in curved spacetime. Since the curvature of the spacetime is small on the scale of the electron's Compton wavelength, the tools of quantum field theory in flat spacetime are reliable and show that a rotating black hole immersed in a magnetic field approaching the quantum critical value of $B_k=m^2 c^3/(e\hbar) \approx 4.4 \times 10^{13}$~G $\approx 1.3\times10^{-11}$ cm$^{-1}$ is unstable. Specifically, a maximally rotating three-solar-mass black hole immersed in a magnetic field of $2.3 \times 10^{12}$~G would be a copious producer of electron-positron pairs with a luminosity of $3 \times 10^{52}$ erg s$^{-1}$.