Abstract
The Lense-Thirring spacetime describes a 4-dimensional slowly rotating approximate solution of vacuum Einstein equations valid to a linear order in rotation parameter. It is fully characterized by a single metric function of the corresponding static (Schwarzschild) solution. In this paper, we introduce a generalization of the Lense-Thirring spacetimes to the higher-dimensional multiply-spinning case, with an ansatz that is not necessarily fully characterized by a single (static) metric function. This generalization lets us study slowly rotating spacetimes in various higher curvature gravities as well as in the presence of non-trivial matter. Moreover, the ansatz can be recast in Painlevé-Gullstrand form (and thence is manifestly regular on the horizon) and admits a tower of exact rank-2 and higher rank Killing tensors that rapidly grows with the number of dimensions. In particular, we construct slowly multiply-spinning solutions in Lovelock gravity and notably show that in four dimensions Einstein gravity is the only non-trivial theory amongst all up to quartic curvature gravities that admits a Lense-Thirring solution characterized by a single metric function.
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Gray, F., Hennigar, R.A., Kubizňák, D. et al. Generalized Lense-Thirring metrics: higher-curvature corrections and solutions with matter. J. High Energ. Phys. 2022, 70 (2022). https://doi.org/10.1007/JHEP04(2022)070
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DOI: https://doi.org/10.1007/JHEP04(2022)070