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Will the event horizons of a two black holes be perturbed or bent before a collision? What will the shape of the event horizon appear to be immediately after first contact?

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There is no contact. –  Ron Maimon Dec 26 '11 at 3:12
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@Ron, that may be technically true, but at some point the system shifts from having two distinct event horizons to having a single event horizon. That point could reasonably be referred to as "contact" IMO. –  Harry Johnston Dec 26 '11 at 3:58
    
@Harry Johnston: The way it happens for a small black hole going into a big one is that the big one gets a little bigger nonlocally a little before the little one hits, and the little one smears over the big horizon. There is no contact. –  Ron Maimon Dec 26 '11 at 10:24
    
@Ron, I suspect the OP is mainly interested in the case of two black holes of similar size. –  Harry Johnston Dec 26 '11 at 20:05
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@RonMaimon: Look at that. We both started telling each other we don't know what we're talking about and in the end we agree. Maybe there is hope for the world. :) –  ThePopMachine Jan 16 '12 at 18:31
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2 Answers

Yes,

Like del piero says, the gravitational field of each one affects the shape of the other, so it's similar to the "metaballs" used in computer graphics.

The exact shape will depend on the geometry, but it usually looks like two fingers reaching out to meet, like in Michelangelo's "The Creation of Adam". You can really see it in the first & last videos here, but there are some good videos of death spirals in between.

Note that the pulsing at the end of the first video isn't anything real; it's caused by the change in magnitude of the color scale shown in the bottom right corner.

There are also a couple of decent still frames (head on collisions of equally massed holes) on these two pages: 1,2.

This one has a shot of asymmetrically massed black holes, just after they join (with the original event horizons drawn underneath):

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The apparent horizon is only affected to the point that the curvature around one black hole is modified by the gravitational field of the other.

The event horizon as defined by the boundary of the causal past of future conformal infinity gets modified in advance of significant changes in curvature, but this precisely what you would expect from a global teleological definition. See Hawking and Penrose for more details.

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