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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 evidence 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 noncircularity, a non-spherically-symmetric event horizon, and violations of the Kerr bound.
Pedro G. S. Fernandes (Mon,) studied this question.