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arXiv · 2112.07649

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

Finnian Gray·Robie A. Hennigar·David Kubiznak·Robert B. Mann·Manu Srivastava
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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 Painlev{\'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 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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Finnian Gray, Robie A. Hennigar, David Kubiznak, Robert B. Mann, Manu Srivastava. 2021-12-14. Generalized Lense--Thirring metrics: higher-curvature corrections and solutions with matter. https://doi.org/10.1007/jhep04(2022)070

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