An Exact Engine for Black-Hole Jets

Abstract

For fifty years the Blandford--Znajek mechanism has been a mechanism and not an exact solution: force-free electrodynamics on a prescribed metric, with the jet's own field carrying no weight. Here that field gravitates. A split monopole weighs as much as a magnetic monopole, so its self-gravity is the magnetic Reissner--Nordström geometry; two copies glued across an equatorial current sheet put hole, disk and jet-driving flux into one spacetime, and force-free plasma makes a magnetosphere of it. Three things then follow that no test-field calculation can see. First, a steady jet is impossible. A stationary horizon cannot be heated but a slipping magnetosphere necessarily heats it, so the only stationary state is a dead one corotating with the hole, and a working jet is a black hole in decay at rates the field equations fix rather than assume. Second, flux enters the laws of black-hole mechanics as a charge, sharing one extremality budget with spin. That budget caps the jet power at $c^5/48G$ whatever the mass. Third, the lifetime output is finite: a maximally spinning hole delivers $1-e^{1/4}/\sqrt{2}=9.2\%$ of its mass and grows its horizon area by exactly $\sqrt{e}$. The horizon's own moment of inertia vanishes with the irrational exponent $(\sqrt{17}-1)/2$ set by the near-horizon throat, and what is left is a rotating hole whose angular momentum has passed to its own field.

17 pages, 5 figures, 1 table. Invited submission to the inaugural issue of "Astronomy Communications", published by the Purple Mountain Observatory, Chinese Academy of Sciences (PMO, CAS) and the University of Science and Technology of China (USTC)