Construction of a Penrose Diagram for an Accreting Black Hole
  A Penrose diagram is constructed for a spatially coherent black hole that accretes at stepwise steady rates as measured by a distant observer from an initial state described by a metric of Minkowski form. Coordinate lines are computationally derived, and radial light-like trajectories verify the viability of the diagram. Coordinate dependencies of significant features, such as the horizon and radial mass scale, are clearly demonstrated on the diagram. The onset of a singularity at the origin is shown to open a new region in space-time that contains the interior of the black hole. 
Beth A. Brown and James Lindesay