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Conformal reference frames for Lorentzian manifolds
I. V. Maresin Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Abstract:
We define a conformal reference frame, i.e., a special projection of the six-dimensional sky bundle of a Lorentzian manifold (or the five-dimensional twistor space) to a three-dimensional manifold. We construct an example, a conformal compactification, for Minkowski space. Based on the complex structure on the skies, we define the celestial transformation of Lorentzian vectors, a kind of spinor correspondence. We express a $1$-form generating the contact structure in the twistor space (when it is smooth) explicitly as a form taking line-bundle values. We prove a theorem on the projection of this $1$-form to the fiberwise normal bundle of a reference frame; its corollary is an equation for the flow of time.
Keywords:
Lorentzian manifold, sky, null geodesic, twistor, contact geometry, line bundle, spinor, conformal symmetry, light cone, Penrose compactification.
Received: 05.04.2016
Citation:
I. V. Maresin, “Conformal reference frames for Lorentzian manifolds”, TMF, 191:2 (2017), 243–253; Theoret. and Math. Phys., 191:2 (2017), 682–691
Linking options:
https://www.mathnet.ru/eng/tmf9202https://doi.org/10.4213/tmf9202 https://www.mathnet.ru/eng/tmf/v191/i2/p243
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Abstract page: | 336 | Full-text PDF : | 124 | References: | 68 | First page: | 27 |
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