Conformal and isometric embeddings of gravitational instantons

Abstract

We construct isometric and conformally isometric embeddings of some gravitational instantons in ${\mathbb{R}}^8$ and ${\mathbb{R}}^7$. In particular we show that the embedding class of the Einstein--Maxwell instanton due to Burns is equal to $3$. For ${\mathbb{CP}}^2$, Eguchi--Hanson and anti-self-dual Taub-NUT we obtain upper and lower bounds on the embedding class.

References in corpus (2)

• Einstein-Maxwell gravitational instantons and five dimensional solitonic strings
• Conformally isometric embeddings and Hawking temperature

Cited by in corpus (3)

• Top-down holography in an asymptotically flat spacetime
• NUTs, Bolts, and Spindles
• Two-sided conformally recurrent self-dual spaces