Rotating Solutions in Critical Lovelock Gravities

TL;DR

This paper constructs exact rotating solutions in critical Lovelock gravities in odd dimensions, revealing new classes of metrics with specific angular momentum configurations and naked singularities.

Contribution

It introduces two classes of explicit rotating metrics in critical Lovelock gravities, expanding the set of known solutions and analyzing their geometric properties.

Findings

Constructed cohomogeneity one rotating metrics with equal angular momenta.

Developed metrics with a single non-zero angular momentum.

Identified naked curvature singularities due to over rotation.

Abstract

For appropriate choices of the coupling constants, the equations of motion of Lovelock gravities up to order n in the Riemann tensor can be factorized such that the theories admits a single (A)dS vacuum. In this paper we construct two classes of exact rotating metrics in such critical Lovelock gravities of order n in d=2n+1 dimensions. In one class, the n angular momenta in the n orthogonal spatial 2-planes are equal, and hence the metric is of cohomogeneity one. We construct these metrics in a Kerr-Schild form, but they can then be recast in terms of Boyer-Lindquist coordinates. The other class involves metrics with only a single non-vanishing angular momentum. Again we construct them in a Kerr-Schild form, but in this case it does not seem to be possible to recast them in Boyer-Lindquist form. Both classes of solutions have naked curvature singularities, arising because of the over rotation of the configurations.