Energy extraction from Kerr--Bertotti--Robinson black holes: polar region collapse and the capture of negative energy protons

Abstract

The Kerr-Bertotti-Robinson black hole is an exact Einstein-Maxwell solution describing a rotating black hole in an asymptotically uniform magnetic field. It differs from the Kerr black hole in the Wald solution: the magnetic field lines are no longer cylindrical, with the constant-\(A_ϕ\) lines saturating at large distances, and the interface \(\vec{E}\cdot\vec{B}=0\) is no longer a cone but contracts with radius and eventually disappears. Determining the acceleration of charged particles pointwise, we find that protons are driven outward and electrons inward in the polar region, and vice versa in the equatorial region; the polar region shrinks as the magnetic field grows. Captured protons carry negative energy and angular momentum, whereas captured electrons carry positive energy and angular momentum. Fixing the capture domain by the gauge-invariant flux criterion and integrating over the \((r,θ)\) plane, we find that in weak magnetic fields the black hole gains mass, while in strong magnetic fields energy extraction occurs. Energy extraction can be achieved under the usual spherically symmetric density, without introducing the anisotropic density distribution required in the Wald solution for a Kerr black hole.