LIGO detects most massive black hole merger to date

I think I'm going to answer my own question by saying both momentum and energy are conserved. The momentum of the entire system was zero before and after the collision. Energy must also be conserved, and since the final object is at rest, all the kinetic energy gets converted into rest mass energy, minus what is radiated away as gravitational waves.

Correct. If you're curious about the 'essence' of what black holes are I actually just did a write-up on them which you can find here: https://photonlines.substack.com/p/an-intuitive-guide-to-bla...

I'm not a physicist, but I took a class on special relativity in college, and I still remember some of it ... If I'm remembering it right, we still have conservation of momentum and energy in special relativity, with the caveat that these are defined differently than in classical mechanics. Specifically, E = γmc^2 and p = mvγ, where γ = 1 / sqrt(1 - v^2/c^2) and m is the invariant mass (aka the "rest mass"). [1] Note that when v=0 (so γ=1), this equation for momentum is the same as the classical p=mv, which is generally a good approximation when v << c.

So, using those relativistic definitions for energy and momentum, I think you're exactly right, at least up to the part about "since the final object is at rest". However:

- As I understand it, invariant mass, aka "rest mass" (which is equivalent to "rest energy", aka "rest mass energy"), is invariant, and it's the same before and after the collision, so the kinetic energy doesn't get "converted into rest mass energy". Rather, if the final object is at rest, then all of its kinetic energy has been radiated away; kinetic energy (E_K) is is total energy (E) minus rest energy (E_0 = mc^2, where m is invariant mass)

- I have no idea whether gravitational waves are the only way for the kinetic energy to be radiated away. I imagine other forms of energy could also be emitted.

- In order to know that the final object is at rest/has no kinetic energy (in an inertial frame), I worry that we might need to have specified more in the original question. In particular, I don't know how to handle spin. (I know that black holes have some concept of "spin", but I don't know if this is like rotational spin, or more like quantum mechanical spin, or something else, and I don't know how it figures into the black holes' total energy.) If we change the original question to say that the black holes are not spinning, then I think we can ignore this (since the collision is head-on).

[1]: https://en.wikipedia.org/wiki/Mass_in_special_relativity#Rel...

To reiterate, I'm not a physicist. I may be off base here, but that's my understanding.

Thanks. Little typo "Let’s inflate Earth once again to its regular size and see what impact placing a 10 kg weight on it has." Should be 1kg.

Thank you - I will correct the mistake!

no, gravitational waves can carry out momentum and energy. This is not a closed system

> Correct

No, outgoing gravitational waves could carry out energy and momentum. This is not a closed system. Nobel prize 1993