The Schwarzschild metric is derived as a Kähler metric on a holomorphic 'coincidence locus' within the twistor space of self-dual Taub-NUT, solving the googly problem for this specific spacetime.
Gluing Noncommutative Twistor Spaces
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abstract
We describe a general procedure, based on Gerstenhaber-Schack complexes, for extending to quantized twistor spaces the Donaldson-Friedman gluing of twistor spaces via deformation theory of singular spaces. We consider in particular various possible quantizations of twistor spaces that leave the underlying spacetime manifold classical, including the geometric quantization of twistor spaces originally constructed by the second author, as well as some variants based on noncommutative geometry. We discuss specific aspects of the gluing construction for these different quantization procedures.
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2026 2representative citing papers
An etale gluing groupoid models the Penrose-Sparling non-Hausdorff twistor space, and a relative cyclic pairing on the Coulomb line bundle recovers the charge n.
citing papers explorer
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Schwarzschild black holes from twistor space
The Schwarzschild metric is derived as a Kähler metric on a holomorphic 'coincidence locus' within the twistor space of self-dual Taub-NUT, solving the googly problem for this specific spacetime.
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Cyclic source pairings for Penrose--Sparling non-Hausdorff twistor spaces
An etale gluing groupoid models the Penrose-Sparling non-Hausdorff twistor space, and a relative cyclic pairing on the Coulomb line bundle recovers the charge n.