Blackhole Ringdown is non-linear and produces Gravitational Waves that interact with themselves

Einstein was so right about many things and his Theory of General Relativity is yet to be contradicted by data.

In this case : since E = mc² or m = E/c² then any form of energy has a mass equivalent ie. energy itself always gravitates in addition to whatever else is happening. That divisor of c² keeps this off the books for most of physics, but with black hole mergers the enormous energy of the waves has a significant mass equivalent - measured in solar masses, say. This gravitates also and produces it own contributions to the turmoil of waves, that in turn have energy and a mass equivalent for that .... etc recursing this self-referential argument to higher orders. That's what's meant by non-linearity. You might think this would give an unbounded energy but in essence the 1/c² comes into play with each higher term ( 1/c⁴, 1/c⁶, 1/c⁸ .... etc ) and the whole summation of effects converges thankfully. Mathematically an infinite number of things may sum towards a finite value. The real thorn in the theory is at the centre of black holes - what's happening there ? GR predicts infinities ( as would Newton for that matter ) and so that is seen as a signal that a more complete theory may apply. Probably quantum mechanics would rule also and may prevent things getting too infinitesimally close together. But don't lose sleep over it. No-one will ever know outside a black hole what is going on inside. Far away from it you will get GR applying quite well, as has been demonstrated by the detectors many times including this work as described.

Cheers, Mike.