Example：10.1021/acsami.1c06204 or Chem. Rev., 2007, 107, 2411-2502
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  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.