Spherical collapse and black hole evaporation

We consider spherically symmetric gravity coupled to a spherically symmetric scalar field with a specific coupling which depends on the Areal Radius. Classical collapse is described by the Vaidya solution. The semiclassical Einstein equations are well defined. Their solution describes an evaporating black hole. A balance law at future null infinity relates the rate of change of a back reaction-corrected Bondi mass to a manifestly positive flux. Its detailed form suggests a quantum extension of future null infinity along which all information including that in the collapsing matter is expected to emerge.