  We present analytic stationary and axially-symmetric black hole solutions to
the semiclassical Einstein equations that are sourced by the trace anomaly. We
also find that the same spacetime geometry satisfies the field equations of a
subset of Horndeski theories featuring a conformally coupled scalar field. We
explore various properties of these solutions, and determine the domain of
existence of black holes. These black holes display distinctive features, such
as non-circularity, a non-spherically symmetric event horizon and violations of
the Kerr bound.
