The paper restates the known factorization Spin(4,C)=(SL(2,C)_L x SL(2,C)_R)/Z2 as a geometric embedding and asserts, without displaying the computation, that contour-regularized Schwarzschild and Kerr metrics yield smooth holomorphic spin connections.
Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten,
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Embedding $\mathrm{SL}(2,\mathbb{C})/\mathbb{Z}_2$ in Complex Riemannian Geometry
The paper restates the known factorization Spin(4,C)=(SL(2,C)_L x SL(2,C)_R)/Z2 as a geometric embedding and asserts, without displaying the computation, that contour-regularized Schwarzschild and Kerr metrics yield smooth holomorphic spin connections.