Geons with spin and charge

TL;DR

This paper constructs new geon-type black holes in higher dimensions with gauge fields, exploring their properties, existence conditions, and including rotating solutions and nonabelian gauge fields.

Contribution

It introduces novel geon constructions in higher-dimensional Einstein and gauge field theories, including rotating and nonabelian cases, expanding the landscape of black hole solutions.

Findings

Existence of static geons with gauge fields depends on spatial isometries.

Rotating geons are found in odd dimensions, not continuously deformable to zero angular momentum in others.

Geons with angular momentum are constructed in AdS with toroidal infinity.

Abstract

We construct new geon-type black holes in D>3 dimensions for Einstein's theory coupled to gauge fields. A static nondegenerate 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 F^2 action can be included by an appropriate (and in most cases nontrivial) 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 nonabelian gauge field, we show that the D=4 spherically symmetric SU(2) black hole admits a geon version with a trivial gauge bundle. Various generalisations, including both black-brane geons and Yang-Mills theories with Chern-Simons terms, are briefly discussed.