English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We compute the contact manifold of null geodesics of the family of spacetimes$\{(\mathbb{S}^2\times\mathbb{S}^1,g_\circ-\frac{d^2}{c^2}dt^2)\}_{d,c\in\mathbb{N}^+\text{ coprime}}$, with$g_\circ$ the round metric on $\mathbb{S}^2$ and $t$ the$\mathbb{S}^1$-coordinate. We find that these are the lens spaces $L(2c,1)$together with the pushforward of the canonical contact structure on$ST\mathbb{S}^2\cong L(2,1)$ under the natural projection $L(2,1)\to L(2c,1)$.We extend this computation to $Z\times \mathbb{S}^1$ for $Z$ a Zoll manifold.On the other hand, motivated by these examples, we show how Engel geometry canbe used to describe the manifold of null geodesics of a certain class ofthree-dimensional spacetimes, by considering the Cartan deprolongation of theirLorentz prolongation. We characterize the three-dimensional contact manifoldsthat are contactomorphic to the space of null geodesics of a spacetime. Thecharacterization consists in the existence of an overlying Engel manifold witha certain foliation and, in this case, we also retrieve the spacetime.

On the space of null geodesics of a spacetime: the compact case, Engel geometry and retrievability