Distorted black holes of the Einstein-Klein-Gordon system

We present two families of solutions (g,Φ) of the Einstein-Klein-Gordon system minimally coupled to gravity, massless scalar field equations possessing a regular RxS2 bifurcating Killing horizon. The solutions may be interpreted as describing the metric g and the field Φ in an open vicinity containing the event horizon of a Schwarzschild black hole interacting with an exterior, static-axisymmetric distribution of matter carrying scalar charges generating Φ. One family of the solution possesses a spherical bifurcation two sphere and may be interpreted as generated by a distribution of matter carrying scalar charges but of negligible self-gravity. The other family describes an axisymmetric horizon with the distortion caused by the self-gravity of the external matter. For both classes of solutions the scalar field Φ relaxes into a configuration so that its energy-momentum tensor Tμν on the Killing horizon obeys the property: Tμνlμlν=0 where lμ is a null vector normal to the horizon. It is also indicated that the Einstein-Klein-Gordon system ought to admit distorted black holes characterized by an RxS1xS1 event horizon