Ricci-flat spacetimes admitting higher rank Killing tensors

TL;DR

This paper constructs Ricci-flat spacetimes with specific signatures that admit higher-rank Killing tensors, using Eisenhart lift and oxidation techniques, revealing new solutions including some that are anti-self-dual in four dimensions.

Contribution

It introduces a novel method to generate Ricci-flat spacetimes with higher-rank Killing tensors via Eisenhart lift and parameter oxidation, expanding the class of known solutions.

Findings

Constructed Ricci-flat spacetimes with rank-3 and rank-4 Killing tensors.

Some four-dimensional solutions are anti-self-dual.

Method applies Eisenhart lift to integrable systems and parameter oxidation.

Abstract

Ricci-flat spacetimes of signature (2,q) with q=2,3,4 are constructed which admit irreducible Killing tensors of rank-3 or rank-4. The construction relies upon the Eisenhart lift applied to Drach's two-dimensional integrable systems which is followed by the oxidation with respect to free parameters. In four dimensions, some of our solutions are anti-self-dual.