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Surface geometry of a rotating black hole in a magnetic field
Phys. Rev. D 33, 2780 – Published 15 May, 1986
DOI: https://doi.org/10.1103/PhysRevD.33.2780
Abstract
We study the intrinsic geometry of the surface of a rotating black hole in a uniform magnetic field, using a metric discovered by Ernst and Wild. Rotating black holes are analogous to material rotating bodies according to Smarr since black holes also tend to become more oblate on being spun up. Our study shows that the presence of a strong magnetic field ensures that a black hole actually becomes increasingly prolate on being spun up. Studying the intrinsic geometry of the black-hole surface also gives rise to an interesting embedding problem. Smarr shows that a Kerr black hole cannot be globally isometrically embedded in if its specific angular momentum a exceeds (√3 /2)m∼0.866. . .m. We show that in the presence of a magnetic field of strength B, satisfying 2- √3 ≤≤2+ √3, a global isometric embedding is possible in for all values of the angular momentum.
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