Conformal geodesics cannot spiral

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• Peter Cameron (University of Edinburgh)
• Wednesday 11 September 2024, 14:00-15:00
• Seminar Room 1, Newton Institute.

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TWTW01 - Twistors in Geometry & Physics

Conformal geodesics are solution curves arising from a conformally invariant equation. These curves have found numerous applications in general relativity. In particular, they have been used to construct conformal Gauss coordinates, which can remain regular across conformal boundaries. In order for such a coordinate system not to break down, it is important that the underlying conformal geodesics do not “spiral” (i.e. enter and remain in every neighborhood of some point). It is a standard fact that this cannot happen for metric geodesics and it has been conjectured that the same is true for conformal geodesics. In this talk I will give a proof (joint with Maciej Dunajski and Paul Tod) that conformal geodesics in Riemannian signature cannot spiral.

This talk is part of the Isaac Newton Institute Seminar Series series.

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