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Twistor action for general relativity

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arxiv 2104.07031 v2 pith:U3DETMKA submitted 2021-04-14 hep-th gr-qcmath-phmath.MP

Twistor action for general relativity

Atul Sharma This is my paper
classification hep-th gr-qcmath-phmath.MP
keywords actiontwistorgeneralrelativitycomplexgravitonpenrosealmost
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We reformulate Euclidean general relativity without cosmological constant as an action governing the complex structure of twistor space. Extending Penrose's non-linear graviton construction, we find a correspondence between twistor spaces with partially integrable almost complex structures and four-dimensional space-times with off-shell metrics. Using this, we prove that our twistor action reduces to Plebanski's action for general relativity via the Penrose transform. This should lead to new insights into the geometry of graviton scattering as well as to the derivation of computational tools like gravitational MHV rules.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Schwarzschild black holes from twistor space

    hep-th 2026-07 conditional novelty 8.0

    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.

  2. Graviton scattering on self-dual black holes

    hep-th 2025-07 unverdicted novelty 8.0

    Exact tree-level MHV graviton scattering amplitudes at arbitrary multiplicity are obtained on self-dual Taub-NUT backgrounds using twistor theory, including spin via Newman-Janis shift, with undeformed celestial symmetries.

  3. Towards a Carrollian Description of Yang-Mills

    hep-th 2026-04 unverdicted novelty 6.0

    A Carrollian theory on null infinity reproduces all MHV and NMHV Yang-Mills tree amplitudes, with a new explicit NMHV expression.

  4. Supersymmetric twists in twistor space and holography

    hep-th 2026-07 unverdicted novelty 5.0

    Computes minimal and chiral algebra twists of supersymmetric self-dual Yang-Mills and N=1 supergravity in twistor space, finding localization to spacetime or planes with matching holographic duals.