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Ambitwistors and Conformal Gravity

  • Claude LeBrun
Part of the NATO ASI Series book series (NSSB, volume 245)

Abstract

In a landmark paper [13] of the 1970’s, Roger Penrose described a remarkable and unexpected connection between Einstein’s equations and the theory of complex manifolds. The twistor correspondence which he detailed there gives a way of producing all self-dual complex solutions of these equations in terms of the global structure of an associated complex manifold called the twistor space. Unfortunately, the most interesting solutions from the view-point of physics are not the self-dual ones, but rather those of Lorentz signature. If this had been the end of the story, one might have therefore been tempted to conclude that this correspondence was merely a mathematical curiosity with no bearing on physics. Fortunately, however, the Penrose twistor correspondence is but one aspect of a rather more complicated story, which I will endeavor to recount here. Indeed, it turns out that the general complex solution of the 4-dimensional Einstein equations can also be described in terms of complex deformation theory, albeit in terms of non-reduced complex spaces rather than complex manifolds.

Keywords

Line Bundle Complex Manifold Twistor Space Null Geodesic Conformal Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Claude LeBrun
    • 1
    • 2
  1. 1.Mathematics DepartmentSUNY Stony BrookUSA
  2. 2.School of MathematicsInstitute for Advanced StudyUSA

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