The idea that black hole spin is instrumental in
the generation of powerful jets in active galactic nuclei and
X-ray binaries is arguably the most contentious claim in
black hole astrophysics. Because jets are thought to origi-
nate in the context of electromagnetism, and the modeling
of Maxwell fields in curved spacetime around black holes
is challenging, various approximations are made in numer-
ical simulations that fall under the guise of ‘ideal magneto-
hydrodynamics’. But the simplifications of this framework
may struggle to capture relevant details of real astrophysical
environments near black holes. In this work, we highlight
tension between analytic and numerical results, specifically
between the analytically derived conserved Noether currents
for rotating black hole spacetimes and the results of gen-
eral relativistic numerical simulations (GRMHD). While we
cannot definitively attribute the issue to any specific approx-
imation used in the numerical schemes, there seem to be nat-
ural candidates, which we explore. GRMHD notwithstand-
ing, if electromagnetic fields around rotating black holes are
brought to the hole by accretion, we show from first princi-
ples that prograde accreting disks likely experience weaker
large-scale black hole-threading fields, implying weaker jets
than in retrograde configurations.

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• Magnetic fields threading black holes: restrictions from general relativity and implications for astrophysical black holes