Before two black holes merge, their individual event horizons must be perfectly spherical due to the No Hair theorem. If they weren't they'd be betraying information about the inside. After merging, the now larger event horizon is also perfectly spherical. However, there is no way I can come up with that gets from before to after without an intermediate non-spherical event horizon that betrays the information that there are two black hole masses inside it in the process of merging. The LIGO simulations show that for a few frames if you slow down the animation. But that's not allowed! Did they fudge that bit? Any thoughts?
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1Related: https://physics.stackexchange.com/q/460041/123208 – PM 2Ring Apr 14 '23 at 03:01
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1Which LIGO simulation? Link? Page? – Qmechanic Apr 14 '23 at 12:09
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The no-hair theorem refers to stationary black hole solutions to the Einstein equations. If the black holes in question are undergoing dynamics, then the no-hair theorem doesn't apply. Specifically, merging black holes enter a ringdown phase in which the distorted spacetime radiates energy away in the form of gravitational waves, leaving a single black hole which is asymptotically "hairless."
It's also worth noting that black hole event horizons are generically not spherical, unless they have no angular momentum - see the Kerr spacetime.

J. Murray
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