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Exotic compact objects with soft hair
  [reference: Raposo, Pani, Emparan, "Exotic compact objects with soft hair", arXiv:1812.07615]:
- Equatorially symmetric solutions 
- Nonequatorially symmetric solutions 
The superscript is the order at which the perturbative solution has been truncated, e.g. [J]^(5) is a purely spin-induced solution up to order five in the spin.

