Workshop From geometry to numerics
IHP, Paris, 20-24 November 2006

José Luis Jaramillo (Inst. Astrofisica de Andalucia, Granada, Spain)

Trapping horizons in constrained evolutions of excised black holes

Starting from the 3+1 description of a Dynamical Horizon, i.e. a world-tube of marginally outer trapped surfaces of increasing area, we discuss a set of boundary conditions caracterizing a space-like sphere as a slice of a Trapping Horizon. These boundary conditions are particularly useful when numerically evolving black holes with a constrained scheme implementing an excision technique, namely with the excised surface coinciding with the black hole (apparent) horizon. Special attention is devoted to the relation between the geometrical choice of dynamical horizon through a given marginally trapped surface, on the one hand, and the choice of spacetime slicing, on the other hand, by means of the the existence and uniqueness theorems for dynamical/trapping horizons.

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