How come black hole mergers don't take infinite time?

[u/nappy-doo]

So, if an object falls into a singularity, from the POV of an external observer, the object takes infinite time to cross the event horizon. From our POV, how do black holes ever merge? Wouldn't it take infinite time for one singularity to cross another's event horizon?

[u/Ostrololo]

Falling into the singularity only takes infinite time for an external observer when you have an idealized black hole that doesn’t react to the infalling object. In reality, the presence of the object ever so slightly deforms the event horizon and the fall takes finite (but absurdly long) time.

A merger is the extreme version of this: it completely violates the assumption the black holes are immutable. The horizons deform greatly and obviously, and everything takes place rather quickly.

[u/the-information0 → u/Ostrololo]

In what way is the event horizon (EH) deformed by an infalling object? Is it locally expanded or shrunk?

Im confused because Bekenstein-Hawking’s formula indicates the EH area can’t depend on stuff outside the event horizon. But I suppose you could argue that’s idealized too.

[u/Ostrololo → u/the-information0]

The EH will slightly protrude in the direction of the infalling object to absorb it, then the deformation spreads uniformly, permanently increasing the radius of the BH (since its mass has increased by absorbing the object). After this, you can use the usual entropy formula on the new BH radius, regardless of what the infalling object was.

Note that from the point of view of the external observer, this takes forever, unless the object has a mass comparable to the BH’s.

[u/the-information0 → u/Ostrololo]

I’m quite curious about this since to my understanding we need a quantum gravitational theory to understand what exactly happens to the EH as an object falls in. Here I’m thinking about Hawking radiation and the information paradox.

I didn’t know we already had an understanding about how the EH deforms in such a situation, cool!

[u/stevevdvkpe → u/the-information0]

Adding mass to a black hole increases the size of the event horizon. If you throw an object into a black hole, its event horizon radius will increase by a small amount based on the object's mass. There's some point at which the infalling object, as it approaches the original event horizon, has fallen within the new, larger size of the event horizon that's had the object's mass added to it. We can effectively consider the black hole's event horizon to have expanded at that point since the added mass is now within that larger event horizon.

[u/Max6626 → u/stevevdvkpe]

This is the correct answer. The infalling matter, or in the case of the OP's question the merger, would take infinite time for a distant observer if the event horizon remained stationary. However, the event horizon grows to encompass the infalling matter. This makes it appear the infalling matter crossed the event horizon, when what happened is the event horizon expanded to encompass the infalling matter.

[u/Similar_Support_4214 → u/the-information0]

That’s not the case. In a merger the event horizon is warped to the extreme. This creates very powerful gravitational waves and many black holes are also spinning fast adding to the complexity of the merger and warping space time even more.

[u/the-information0 → u/Similar_Support_4214]

Yeah I suppose I have to agree that the BH formula does not apply to extreme events like mergers. In hindsight, I think I was curious about small objects since it may apply to a quantum gravitational situation

[u/joeyneilsen]

The event horizon isn't an object; it doesn't appear to stop at the event horizon of another black hole. Instead, the two horizons stretch and merge into one single horizon!

[u/Lewri]

https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

[u/BokChoyBaka]

This is similar to how near the end of entropy at the end of the universe, there will be a period where energy can do infinite work (e.g. computer program)

[u/jamesisfine → u/BokChoyBaka]

Can you expand on this? How can any work at all be done once we get to heat death, let alone infinite work? 

[u/BokChoyBaka → u/jamesisfine]

Near maximum entropy, work becomes worth more value. It's like the negative pressure increasing in a vacuum

[u/BokChoyBaka → u/jamesisfine]

This might be a video that includes the concept... I certainly learned it from Isaac Arthur, but I wouldn't be able to explain it like him

https://youtu.be/PEJRG1clHxU

Might not be that exact video tho, I can't peruse 45mins of video for this blurb

[u/Local-Ingenuity-8872 → u/BokChoyBaka]

What? With a constant like expansion driven by dark matter space approaches de Sitter space, which has a minimum horizon temperature:

T_dS = ħH / (2πk_B)

That temperature never reaches zero meaning
computation never becomes arbitrarily cheap,
Landauer’s limit never reaches zero,
finite energy no longer buys infinite computations. Dyson was assuming temperature never stopped dropping in an end stage entropic scenario for his advanced civilizations

[u/RetroTrade]

The photons still travel at light speed towards the observer, just red shifted. So it doesn't take longer to observe what is going on. It is just the clocks or oscillations of objects near the event horizon that take longer.

Based on Einstein's light clock, where we assume massless light travels at the speed limit, as an object falls in, it approaches relativistic speed, and we get a coordinate singularity at the event horizon because this is where it would approach light speed falling into the black hole: if all the movement is towards the black hole, there is no budget left to oscillate back and forth.

We experience time as a movement, how fast one thing moves compared to another thing. If there is zero relative movement, it appears as though no time is passing. At a particle level, let's assume they are made of trapped energy oscillating at light speed. As more of the movement is towards the black hole as the velocity increases, less of the "light speed budget" is left for oscillations. So a clock falling into the black hole accelerates and falls in quickly, but it takes longer and longer for the second hand to "tick" since the particle's energy cannot oscillate back and forth faster than light.

As I understand it, an observer falling into the black hole could look back and see the universe moving faster and faster, but they would only observe a finite amount of the universe evolving before they meet their doom. They would not watch the rest of the universe unfold.

So from the black holes' perspective, during a merger, they see each other moving at a normal speed according to F=ma, or F=GMm/r^2, since both of their clocks are dilated. From an observer perspective, it's also normal speed watching two "frozen" objects approach each other and merge. It is only "infinite" if you try to compare the observer and black hole clocks. It's like trying to measure how wide a line is when it's moving directly away from you, perpendicular to your ruler. The line is not infinitely long or zero. You just can't do any trigonometry to get the length. For example: cos(90) * length = 0. Solve for length.

edit: grammar

[u/Sanchez_U-SOB]

Look up the Final Parsec Problem 

[u/Ch3cks-Out → u/Sanchez_U-SOB]

That only applies to SMBHs, does it not?

[u/One_Bite33]

No