The NLO/NNLO small-c (Carroll) expansion of GR admits a rich stationary vacuum sector with rotating Lense-Thirring-type, C-metric-type, Hartle-Thorne-type, and higher-multipole solutions, going beyond the static magnetic Carroll truncation.
Henneaux,Geometry of Zero Signature Space-times,Bull
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Stationary solutions in the small-$c$ expansion of GR
The NLO/NNLO small-c (Carroll) expansion of GR admits a rich stationary vacuum sector with rotating Lense-Thirring-type, C-metric-type, Hartle-Thorne-type, and higher-multipole solutions, going beyond the static magnetic Carroll truncation.