History of a black hole horizon

The most dynamic changes in a black hole horizon occur as the black hole is forming and before it settles into a stationary state. The definition of the event horizon and the properties of null hypersurfaces imply that the horizon is generated by null geodesics, which enter the horizon at a "crease set." This acausal and typically 2-dimensional and finite set can be regarded as the horizon's origin. But in a physically motivated time sequence the horizon starts at a lower-dimensional subset of the crease set and can assume various topologies during its history, depending on how the time sequence slices up the spacetime, and on the possible branchings of the crease set. An alternative description of the horizon propagates it backwards in time from its spherical shape at large times through self-intersecting surfaces, which can represent topological changes smoothly. A number of examples are given, which illustrate some of the possible changes in the horizon's early history.