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-Aϕ lines saturating at large distances, and the interface E⃗·B⃗=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.
Related
- On the Extended Kerr-Newman-Bertotti-Robinson Spacetime: Two Black Holes and a Naked Singularity in Bertotti-Robinson Universe
- Thermodynamics of Kerr-Bertotti-Robinson black hole
- From Bertotti–Robinson to vacuum: New exact solutions in general relativity via Harrison and Inversion symmetries
- Dynamics, ringdown, and accretion-driven multiple quasi-periodic oscillations of Kerr–Bertotti–Robinson black holes
- Reissner-Nordstrom in the Bertotti-Robinson-Bonnor-Melvin electromagnetic field
BibTeX
@misc{wang2026energy,
title = {{Energy extraction from Kerr--Bertotti--Robinson black holes: polar region collapse and the capture of negative energy protons}},
author = {Ke Wang and Xiao-Xiong Zeng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32494},
eprint = {2609.32494},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32494},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Energy extraction from Kerr--Bertotti--Robinson black holes: polar region collapse and the capture of negative energy protons
AU - Ke Wang
AU - Xiao-Xiong Zeng
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32494
UR - https://arxiv.org/abs/2609.32494
AB - 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 E⃗·B⃗=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.
ER -