Conformal representation of Kerr space-time poloidal sub-manifolds
2020
We use two conformal transformations to represent field lines in the poloidal sub-manifold of Kerr space–time. The first one is based on an embedding in of a manifold which is conform to the poloidal submanifold. The second one is a planar representation using quasi-isotropic coordinates. We compare plots of the poloidal magnetic field lines in the usual Boyer–Lindquist Cartesian coordinates and in the conformal representation based on quasi-isotropic coordinates. In a conformal representation these lines appear entering in the horizon perpendicularly to it as deduced through a mathematical perspective conversely to the usual physical approach. We also compare the value of the conformal factor in these two representations.
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