Rotating solutions in critical Lovelock gravities. (English) Zbl 1369.83072
Summary: 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 admit 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 \(d = 2 n + 1\) 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.
MSC:
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83C20 | Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory |
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