Conformal reference frames for Lorentzian manifolds
Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 2, pp. 243-253
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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.
@article{TMF_2017_191_2_a8,
author = {I. V. Maresin},
title = {Conformal reference frames for {Lorentzian} manifolds},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {243--253},
publisher = {mathdoc},
volume = {191},
number = {2},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a8/}
}
I. V. Maresin. Conformal reference frames for Lorentzian manifolds. Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 2, pp. 243-253. http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a8/