Some uniqueness results for dynamical horizons
The authors carefully discuss the several possibilities to define the horizon of a black hole. The most famous one via the event horizon, is often impracticable as the location of the event horizon depends on the geometry at infinity. This is especially inconvenient to apply when one wants to make numerical calculations near the horizon. Therefore, the authors propose to use the notion of a DH (dynamical horizon), this is by definition a spacelike and marginally trapped tube. The idea behind this notion is the following: Starting with two black holes which, in the beginning, are at rest at a large distance from each other, then one expects gravity to attract them such after a while, both black holes should coalesce to form one single black hole. This procedure can already be calculated in great detail by numerical methods. Then the dynamical horizon consists first of two spheres, then the trapped tube, and finally one sphere. The present paper concentrates on the non-uniqueness of the definiton of a DH and how to overcome it, and it makes several comments on the relation to quantum gravity and numerical relativity. One of the sections deals with the case that at least one Killing vector exists.
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