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The waveforms are predicted by our knowledge of general relativity; specifically what the gravitational wave profile would be for two objects of certain masses spiraling into each other.

A semi-hand-wavy way we know that the objects in this particular inspired are black holes is that for them to be orbiting each other this fast, they must be very close. For them to be this close, they must be very small. Together, this implied the objects have a certain size which is smaller than their Schwarzschild radius, which means they are probably black holes.

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