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 c5/48G whatever the mass. Third, the lifetime output is finite: a maximally spinning hole delivers 1−e1/4/√2=9.2% of its mass and grows its horizon area by exactly √e. The horizon's own moment of inertia vanishes with the irrational exponent (√(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.
Related
- The compact jets of the black hole X-ray binary Swift J1753.5-0127 during its 2023-2024 outburst
- Nonuniform Particle Injection into Black Hole Jets by Radiative Magnetic Reconnection
- Jets from a stellar-mass black hole are as relativistic as those from supermassive black holes
- Multimessenger Constraints on the Central Engine in SN 2023ixf: Neutron Star or Black Hole?
- A Self-Sustaining Black Hole Engine Powered by the Tidal Disruptions of Stars
BibTeX
@misc{wang2026exact,
title = {{An Exact Engine for Black-Hole Jets}},
author = {Yu Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02742},
eprint = {2609.02742},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02742},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Exact Engine for Black-Hole Jets
AU - Yu Wang
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02742
UR - https://arxiv.org/abs/2609.02742
AB - 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/√2=9.2% of its mass and grows its horizon area by exactly √e. The horizon's own moment of inertia vanishes with the irrational exponent (√(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.
ER -