Plasmoid-mediated Penrose extraction as a parallel energy channel — compare reconnection power to BZ jet power at the same spin and field (Meringolo et al. 2025)
The Blandford-Znajek (1977) mechanism extracts rotational energy from a Kerr black hole electromagnetically via a large-scale field threading the horizon. In SI units:
r_g = GM/c² (gravitational radius; the Schwarzschild radius is 2r_g)
r_+ = r_g(1 + √(1 − a²)) (outer horizon)
Ω_H = ac/(2r_+) (horizon angular velocity)
P_BZ = (κ/4πμ₀) B² r_+⁴ Ω_H²/c, where κ = 0.044 (numerical factor)
In plasmoid-mediated reconnection the current sheet near the ergosphere boundary breaks into a chain of magnetic islands (plasmoids), dramatically accelerating the reconnection rate. The energy tap is approximately:
P_rec ≈ 1.646 × η_rec × a*² × P_BZ
This is a phenomenological calibration to the Meringolo et al. (2025) GRPIC result that reconnection contributes ~10–30% of P_BZ at spin a* > 0.9. The factor 1.646 is fixed so that η_rec = 0.15 at a* = 0.9 gives exactly 20% of P_BZ. The reconnection efficiency η_rec is the reconnection inflow speed as a fraction of the Alfvén speed; the Meringolo 2025 GRPIC runs find a median of ~0.15 at high spin. (An earlier analytic formula P_rec = η(B²/2μ₀)πrg²c overestimated by ~160× because the effective reconnecting layer area is far smaller than the full ergosphere cross-section.)
BZ extracts energy via the Poynting flux of the global magnetosphere threaded through the horizon. Reconnection extracts energy locally in the current sheet where field lines of opposite polarity annihilate; the liberated magnetic energy goes partly into particle kinetic energy (some of which escapes) and partly into electromagnetic radiation. In the Kerr geometry both channels draw on the same reservoir — the spin energy of the hole — but via distinct pathways that operate simultaneously. For engineering purposes they sum as parallel power channels with the same magnetic field as fuel.
The theoretical maximum fraction of rest-mass energy extractable via Penrose-class processes (Penrose 1969) is η_max = 1 − √((1 + √(1−a²))/2). At a=0.998 this reaches ~20.7%; at a=0.9 it is ~15.6%. The reconnection efficiency η_rec is a different quantity — it is the rate parameter of the reconnection layer, not a thermodynamic bound — but both quantities are shown here for context.
Comisso & Asenjo (2021, Phys Rev D 103:023014) studied reconnection driven by field-line ergospheric crossing in the equatorial plane — a topological mechanism. Meringolo et al. (2025) studied GRPIC simulations of plasmoid-instability reconnection in the magnetosphere above the ergosphere. The two papers describe different physical processes and should not be combined or confused. This calculator implements the Meringolo 2025 prescription.
10⁴ T: extreme laboratory (pulsed). 10⁶–10⁸ T: neutron-star interior estimates. 10⁸–10¹¹ T: magnetar surface. The equatorial field threading an accreting IMBH horizon is model-dependent but GRMHD magnetically-arrested disk (MAD) simulations suggest B ~ (10⁴–10⁶) T for an 8,200 M☉ hole accreting near the Eddington rate. The default 10⁶ T is optimistic but not physically excluded.