Geons with spin and charge

We construct new geon-type black holes in D ⩾ 4 dimensions for Einstein's theory coupled to gauge fields. A static non-degenerate vacuum black hole has a geon quotient provided the spatial section admits a suitable discrete isometry, and an antisymmetric tensor field of rank 2 or D − 2 with a pure F2 action can be included by an appropriate (and in most cases non-trivial) choice of the field strength bundle. We find rotating geons as quotients of the Myers–Perry(-AdS) solution when D is odd and not equal to 7. For other D we show that such rotating geons, if they exist at all, cannot be continuously deformed to zero angular momentum. With a negative cosmological constant, we construct geons with angular momenta on a torus at the infinity. As an example of a non-Abelian gauge field, we show that the D = 4 spherically symmetric SU(2) black hole admits a geon version with a trivial gauge bundle. Various generalizations, including both black-brane geons and Yang–Mills theories with Chern–Simons terms, are briefly discussed.