Relativity and gravitational theory Definition

Blandford–Znajek process

Builds on Force-free magnetic field Maxwell's equations Schwarzschild metric

Definition

Let $G$ be the gravitational constant and $c$ the speed of light. Let a Kerr black hole of mass $M$ have dimensionless spin $a \in (0, 1)$ and horizon radius $r_H = (GM/c^2)(1 + \sqrt{1 - a^2})$ . Its horizon angular velocity is $\Omega_H = a c / (2 r_H)$ . Let a stationary, axisymmetric magnetosphere surround the hole, and let some of its field lines cross the horizon. Its electromagnetic field solves Maxwell's equations on the Kerr spacetime and is force-free. In such a field each field line rotates rigidly with an angular velocity $\Omega_F$ , constant along the line. The Blandford–Znajek process is the outward flux of electromagnetic energy through the horizon along the field lines with $0 < \Omega_F < \Omega_H$ . The rotational energy of the hole pays for this flux.

Remarks

On a field line crossing the horizon the outward energy flux is proportional to $\Omega_F (\Omega_H - \Omega_F)$ , so it is positive exactly when $0 < \Omega_F < \Omega_H$ and is largest for $\Omega_F = \Omega_H / 2$ . For a magnetic flux $\Phi$ through the horizon, the total power has the form $P \approx \kappa \, \Phi^2 \Omega_H^2 / c$ in Gaussian units, with a dimensionless factor $\kappa$ that depends on the field geometry.

Example: in the slowly rotating split monopole field of the original paper, the field lines rotate at about $\Omega_H/2$ , and energy flows out to infinity along all of them.

Non-example: a non-rotating hole, with the Schwarzschild metric, has $\Omega_H = 0$ ; no $\Omega_F$ satisfies $0 < \Omega_F < 0$ , so there is no Blandford–Znajek power.

The process is often compared with the Penrose process, since both draw on the rotational energy of the hole.

Reading path

To understand this page from the ground up, read these 5 pages in order. The foundations come first.

Show the path as a graph

Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.

no evidence level

Tag	`PEMQHB13Q3`
URI	`m2://PEMQHB13Q3`
Kind	definition
Writing	W0 stub
MSC	83C57, 85A30, 76W05
Defines	Blandford–Znajek process
Uses	Force-free magnetic field, Maxwell's equations, Schwarzschild metric
Changed	3 November 2026

Blandford–Znajek process

Definition

Remarks

Reading path

Further reading

What this page needs for W1

What links here