Echoes Beyond the Horizon: Gravitational Secrets?

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Could gravitational waves from colliding black holes carry echoes of their internal structure, revealing what's inside without ever looking?
I get what you’re trying to say, but it’s not quite right as stated. The quadrupole moment is the source of gravitational radiation, yes, but for anything other than black holes the quadrupole does depend on internal structure.
If you already knew the answer, why did you ask the question?
 
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