Ask HN: Mass Loss in Black Hole Merger? How Does That Work? | Hacker News Reader

Ask HN: Mass Loss in Black Hole Merger? How Does That Work?

6 pointsAnimalMuppet4 comments

Let's say we have two black holes, one 20 solar masses and the other 50 solar masses, and they get close enough and merge. In the process, they convert a solar mass or two into gravitational waves, which radiate off into the distance.

Let me restate that, to emphasize what I think is really weird: A solar mass or two that is inside the event horizon got converted to energy and radiated outside the event horizon.

E=mc^2. That part doesn't bother me. It's the "inside the event horizon" to "outside the event horizon" part that bothers me. Can someone ELI5 how that is possible? (Or even ELI20 with an undergrad in physics.)

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The black hole has more energy inside it than the component parts. That energy includes the gravitational binding energy, which is not "inside" of the black hole. It never passed through the event horizon to get there.

So when the black holes merge, they lose some of their gravitational binding energy as the insides fall in to one another. Nothing that passed through the event horizon gets lost.

Another way to look at it: imagine you have two counter-spinning black holes. When they collide, the net momentum is now zero, but energy must be conserved. That angular momentum was never really inside the black hole in the first place, so nothing passes through the event horizon to escape it.

The gravitational binding energy and angular momentum are different kinds of energy, but they illustrate the same idea.

Sorry, I am not informed about general relativity, but I can say this: the mass (and the angular momentum, and the electric charge IIRC) are all ‘visible’ through the event horizon - indeed, if they weren’t, the a black hole would in some sense wink out of existence as it formed - no gravitational pull, no frame-dragging.

I am oversimplifying, and treating the black hole as already collapsed inside the event horizon from the point of view of somebody well away from it; that’s not accurate. Perhaps thinking of that mass as being ‘just about to collapse into the event horizon’ is the best way to think about it, because that’s what that somebody would perceived from the outside who is not in free-fall into it.

Need a proper physicist to follow up on this, my training stopped at special relativity and Newtonian gravity…

(PS: studying tensor calculus and general relativity is on my bucket list - thanks for reminding me to get a move on with it!)

I'm a layman but as I understand it Hawking radiation (which is what we seem to be discussing) is a consequence of quantum mechanics and uncertainty - it isn't actually possible for a black hole to capture all of the energy that falls into it because the vacuum itself contains random quantum fluctuations of energy states which can result in energy escaping the black hole (although not information) through quantum tunneling, increasing entropy.

https://en.wikipedia.org/wiki/Hawking_radiation

No, we're not talking about Hawking radiation. Hawking radiation is particles and, for medium-to-large black holes, it's very slow. We're talking about the gravitational waves generated by a black hole merger, most of which are generated in seconds.

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