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Stationary axisymmetric black holes with matter
Communications in Analysis and Geometry  (IF0.736),  Pub Date : 2021-01-01, DOI: 10.4310/cag.2021.v29.n1.a2
Otis Chodosh, Yakov Shlapentokh-Rothman

We provide a geometric framework for the construction of non-vacuum black holes whose metrics are stationary and axisymmetric. Under suitable assumptions we show that the Einstein equations reduce to an Einstein-harmonic map type system and analyze the compatibility of the resulting equations. This framework is fundamental to our construction [3] of metric-stationary axisymmetric bifurcations of Kerr solving the Einstein–Klein–Gordon system, and as such, we include specializations of all of our formulas to the case of a time-periodic massive scalar field.