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The Lense--Thirring spacetime describes a 4-dimensional slowly rotatingapproximate solution of vacuum Einstein equations valid to a linear order inrotation parameter. It is fully characterized by a single metric function ofthe corresponding static (Schwarzschild) solution. In this paper, we introducea generalization of the Lense--Thirring spacetimes to the higher-dimensionalmultiply-spinning case, with an ansatz that is not necessarily fullycharacterized by a single (static) metric function. This generalization lets usstudy slowly rotating spacetimes in various higher curvature gravities as wellas in the presence of non-trivial matter. Moreover, the ansatz can be recast inPainlev{\'e}--Gullstrand form (and thence is manifestly regular on the horizon)and admits a tower of exact rank-2 and higher rank Killing tensors that rapidlygrows with the number of dimensions. In particular, we construct slowlymultiply-spinning solutions in Lovelock gravity and notably show that in fourdimensions Einstein gravity is the only non-trivial theory amongst all up toquartic curvature gravities that admits a Lense--Thirring solutioncharacterized by a single metric function.

Generalized Lense--Thirring metrics: higher-curvature corrections and solutions with matter