1:Apparent Horizons
Apparent horizons are locatable with data at one instant of time. That is, they are local objects in contrast to event horizons which are global objects.
Apparent horizons provide an ideal surface for excision of the black hole singularity. Points inside the apparent horizon are causally disconnected from points exterior to it. Hence we use it to excise the curvature singularity within black holes.
The apparent horizon is defined by the solution of an elliptic equation.