Meissner effect in Kerr–Bertotti–Robinson spacetime
- 1Universitas Katolik Parahyangan
Abstract
We study the black-hole Meissner effect for extremal Kerr–Bertotti–Robinson (Kerr–BR) black holes, exact Einstein–Maxwell solutions describing a rotating black hole immersed in a uniform Bertotti–Robinson electromagnetic universe. We show that extremality alone is not sufficient for complete magnetic-flux expulsion in this family. For a purely magnetic external BR field, finite extremal holes with 0 carry the exact northern−hemisphere flux\Phi _N=-2\pi Ba^2\sqrt{1-B^2a^2}, which is nonzero and maximal in magnitude atBa=1/\sqrt{2}. Complete expulsion occurs only in the static near−horizon boundary limitBa\rightarrow 1^-, equivalentlyk\rightarrow 0, where the U(1) fibration of the near−horizon metric trivialises. The proof relies on two exact identities that hold at extremality for all values of the external field,\Omega _x|_{r_e}=0and\Omega _r|_{r_e}=B^2a, both consequences of the double−root structure of the horizon function\Delta . Together they force the azimuthal potentialA_\phi |_{r_e}in the purely magnetic sector to become independent of the polar angle in the static boundary limit, so that the gauge−invariant horizon flux densityF_{x\phi }|_{r_e}$$ and the flux through any smooth horizon cap vanish. The Kerr–BR result is contrasted with the Kerr–Melvin family, where the static limit occurs at a finite interior field strength, and with the Melvin–Kerr–Newman–Taub–NUT spacetime, where the NUT parameter is known to prevent expulsion. A complementary throat-geometry argument and qualitative implications for Blandford–Znajek jet suppression near the static boundary of the extremal branch are discussed.
Related
- On the Extended Kerr-Newman-Bertotti-Robinson Spacetime: Two Black Holes and a Naked Singularity in Bertotti-Robinson Universe
- Global structure and stability of Kerr-Bertotti-Robinson spacetime
- External magnetic-field effects on dipolar-particle orbits and critical collisions in Kerr--Bertotti--Robinson spacetime
- Dynamics, ringdown, and accretion-driven multiple quasi-periodic oscillations of Kerr–Bertotti–Robinson black holes
- Local tests of Schwarzschild-Bertotti-Robinson spacetime
BibTeX
@article{siahaan2026meissner,
title = {{Meissner effect in Kerr–Bertotti–Robinson spacetime}},
author = {Haryanto M. Siahaan},
journal = {The European Physical Journal C},
year = {2026},
month = nov,
doi = {10.1140/epjc/s10052-026-16539-6},
url = {https://link.springer.com/article/10.1140/epjc/s10052-026-16539-6},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Meissner effect in Kerr–Bertotti–Robinson spacetime
AU - Haryanto M. Siahaan
PY - 2026
DA - 2026/11/06
JO - The European Physical Journal C
DO - 10.1140/epjc/s10052-026-16539-6
UR - https://link.springer.com/article/10.1140/epjc/s10052-026-16539-6
AB - We study the black-hole Meissner effect for extremal Kerr–Bertotti–Robinson (Kerr–BR) black holes, exact Einstein–Maxwell solutions describing a rotating black hole immersed in a uniform Bertotti–Robinson electromagnetic universe. We show that extremality alone is not sufficient for complete magnetic-flux expulsion in this family. For a purely magnetic external BR field, finite extremal holes with 0 carry the exact northern−hemisphere flux\Phi _N=-2\pi Ba^2\sqrt{1-B^2a^2}, which is nonzero and maximal in magnitude atBa=1/\sqrt{2}. Complete expulsion occurs only in the static near−horizon boundary limitBa\rightarrow 1^-, equivalentlyk\rightarrow 0, where the U(1) fibration of the near−horizon metric trivialises. The proof relies on two exact identities that hold at extremality for all values of the external field,\Omega _x|_{r_e}=0and\Omega _r|_{r_e}=B^2a, both consequences of the double−root structure of the horizon function\Delta . Together they force the azimuthal potentialA_\phi |_{r_e}in the purely magnetic sector to become independent of the polar angle in the static boundary limit, so that the gauge−invariant horizon flux densityF_{x\phi }|_{r_e}$$ and the flux through any smooth horizon cap vanish. The Kerr–BR result is contrasted with the Kerr–Melvin family, where the static limit occurs at a finite interior field strength, and with the Melvin–Kerr–Newman–Taub–NUT spacetime, where the NUT parameter is known to prevent expulsion. A complementary throat-geometry argument and qualitative implications for Blandford–Znajek jet suppression near the static boundary of the extremal branch are discussed.
SN - 1434-6052
ER -