# Do black hole singularities actually merge?

new questioner here so please be gentle.

Do the singularities of merging black holes actually merge together? I mean there are 2 infinitely small objects (singularities) that are trying to find each other but for them to merge they have to join at the EXACT same point in space. I know they can get close, but to expect them to align perfectly with zero tolerance seems impossible.

• I think the broad stroke of the answer is: it's the event horizons that merge, not (necessarily) the singularities. Feb 18, 2016 at 0:15
• I rather like this question cause it's both, simple and at the same time, probably impossible to answer. A problem lies in defining what a singularity is. See physics.stackexchange.com/questions/3892/… But if you define singularities as infinitely small points which they may or may not be, would the two infinitely small points meet or will they only spiral ever closer? That's an interesting mathematical question that makes me think of Zeno and his silly paradox. Feb 18, 2016 at 15:27

## 1 Answer

Infinities are hard to bend the mind around, but in this case, the merge is not impossible. Yes, the distance between them must reach zero in order to make the black holes merge, but the rate of which energy is lost to gravitational waves also increases when they get close to each other.

We are therefore dealing with a $\frac{\mathrm{infinity}}{\mathrm{infinity}}$ problem, where a finite limit may, and in this case does exist.

Do not forget your $\lim$'s!

• So what's this limit? Cuz for me it seems like this limit should rather give some informaton on how efficient the black holes merge.. thus giving information on internal energy dissipation processes, as opposed to other popular science... Feb 18, 2016 at 0:40
• Assuming energy is lost in that way, with the escape velocity greater than c, wouldn't energy from gravity waves also spiral inside towards the center, not outwards and away? Perhaps kind of like a water wave trying to carry water up a waterfall? I do rather like your approach to this question though. Feb 18, 2016 at 15:28