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Do the interiors of black-holes create gravitational waves and if so do these waves cause the radius of the event horizon to fluctuate as the waves pass the horizon ?

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Distortions of the horizon do cause gravitational waves to radiate, an effect known as the 'ringdown' of the black hole horizon.

Effects happening inside of the interior of the blackhole cannot cause distortions of the horizon.

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Just some notes: Ringdown is the result of binary coalescence specifically. The fluctuations of the event horizon are called quasi-normal modes (QNMs). QNMs may be induced by any perturbative process (including ringdown but also, for example, a gravitational wave passing the black hole (BH) or by collapse to a BH). This is a nice (but technical) review. –  user12345 Sep 11 '12 at 20:08
    
Why does the horizon not get distorted by things happening in the interior, is it because gravitational waves for example, if they originate from the interior of the black should be mapped by the ADS/CFT correspondance to the horizon ? Or why is this if I am wrong? Just curious... –  Dilaton Sep 11 '12 at 21:14
    
@Dilaton: The gravitational disturbances have to obey the same laws that everything else does. Once inside the black hole, there is no future-pointing path that travels to the outer horizon. No need to evoke anything as esoteric as AdS/CFT –  Jerry Schirmer Sep 11 '12 at 21:23
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@Dilaton “He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever” :) –  user12345 Sep 12 '12 at 9:49
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@Dilaton: there was nothing stupid above. Trying to understand is not stupid. –  Jerry Schirmer Sep 12 '12 at 16:34
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