Conformal representation of Kerr space–time poloidal sub-manifolds

Loïc Chantry (1) , Véronique Cayatte (1) , Christophe Sauty (2, 1)

1 LUTH (UMR_8102) - Laboratoire Univers et Théories
2 LUPM - Laboratoire Univers et Particules de Montpellier

We use two conformal transformations to represent eld lines in the poloidal sub-manifold of Kerr space-time. The rst one is based on an embedding in R 3 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 eld 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.

Mots clés: poloidal submanifold; general relativity; conformal representation

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Planète et Univers [physics]; Physique [physics]; Astrophysique [astro-ph]

Loïc Chantry, Véronique Cayatte, Christophe Sauty. Conformal representation of Kerr space–time poloidal sub-manifolds. Classical and Quantum Gravity, 2020, 37 (10), pp.105003. ⟨10.1088/1361-6382/ab8399⟩. ⟨hal-03035891⟩