LIGO detects most massive black hole merger to date

They would merge and produce a black hole with the sum of their momentums

Because nothing can ever leave the event horizon black holes are essentially perfectly sticky.

So, if two black holes, each with mass M, were moving at nearly the speed of light and collided head-on (resulting in a final velocity of zero), what would happen to all that momentum? Would the resulting black hole have a mass greater than 2M? If so, how and why would this occur?

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.

My hunch is they would briefly pancake and much of the mass/energy contribution from their initial velocities would dissipate as incredibly high amplitude gravitational waves from the ring-down.

> Because nothing can ever leave the event horizon black holes are essentially perfectly sticky.

If Hawking radiation turns out to be non existent, yes.

Also, we don't know if it's possible to 'crack' open a black hole. If anything, another black hole might be the perfect instrument for doing this.

When you say cracking open a black hole do you mean cracking the event horizon to form a naked singularity?

Hawking radiation occurs because black holes are sticky ‼

It would create a universe, obviously. First all the mass would attempt being squished at a singularity. WHILE the squishing continues, the first-in-line stuff would've already started to explode back-out inside the event horizon. From the inside viewpoint, this looks like the big bang. Once all the mass from the two black holes collide and loose momentum, the inside-universe no longer expands as fast. Things wobble a bit as all this happens, creating tangles and non-homogeneity. Could be caused by initial Planck-scale uncertainties even when having a perfect head-on collision.

The answer would likely be worth a Nobel prize or two.

Huh nice analogy

Energy and momentum are always conserved in EVERY physical process. We can distinguish three types of collisions: “sticky” ones, in which the kinetic energy decreases (typically, it is converted into heat); “explosive” ones, where the kinetic energy increases; and elastic ones, in which the kinetic energy is conserved. Since the total energy (rest plus kinetic) is always conserved, it follows that rest energy (and hence also mass) increases in a sticky collision, decreases in an explosive collision, and is unchanged in an elastic collision. The resulting black hole in other words would have way more of a mass than 2M since you're talking about a 'sticky' collision in the above instance. You can see an example of why this is in Griffiths' text (Introduction to Elementary Particles (which I highly recommend)) -- page 101 contains a great example of what happens to the mass of particles in 'sticky' collisions: https://www.hlevkin.com/hlevkin/90MathPhysBioBooks/Physics/Q...

> black holes are essentially perfectly sticky

Black Hole brand adhesive: when you absolutely, positively need something stuck down for eternity.

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.

> Energy and momentum are always conserved in EVERY physical process.

Veritasium recently claimed otherwise https://www.youtube.com/watch?v=lcjdwSY2AzM

They would cancel each other out and disappear, like a snake eating its own tail.

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.

That is about something entirely different. It more or less just says that energy might be lost if you have a flux towards infinity. It does not in any way claim e.g. that the divergence of the stress energy tensor is non-zero (which would be how I think most people would interpret energy/momentum conservation).

What if the collision was only a grazing one, not head on?

Would they still fully merge, or might you get a mass exchange between them? Or even a smaller black hole spun off?

To answer my own question, some lay research shows it seems it is technically possible for them not to merge if only a tiny portion of their apparent event horizons merge and for only very briefly.

But this is because of a distinction between the Apparent Horizon [1] (which is coordinate-dependent) and the true global event horizon. So they appear to briefly merge but no true global event horizon forms to encompass both. I think!

[1] https://physics.stackexchange.com/questions/38721/what-is-th...

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