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arXiv · 2406.01800

Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds

Jack Borthwick·Yannick Herfray
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Abstract

In this article we discuss how to construct canonical \emph{strong} Carrollian geometries at time/space like infinity of projectively compact Ricci flat Einstein manifolds $(M,g)$ and discuss the links between the underlying projective structure of the metric $g$. The obtained Carrollian geometries are determined by the data of the projective compactification. The key idea to achieve this is to consider a new type of Cartan geometry based on a non-effective homogeneous model for projective geometry. We prove that this structure is a general feature of projectively compact Ricci flat Einstein manifolds.

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Jack Borthwick, Yannick Herfray. 2024-06-03. Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds. https://doi.org/10.1007/s10711-024-00973-5

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