Black Hole Tensile Strength: What Happens at Planck's Length?

[hexexpert]

Forgive the title.

Long ago I was told that if two black hole traveling rapidly relative to each other "brushed" past each other they'd pull each other in. I find it odd that a massive object traveling near the speed of light would suddenly stop dead in its track.

Instead consider two black hole traveling past each other at high speed with a "good" amount of distance between. At the point of nearest approach a number of other smallish black holes, coming from various directions, intersect the straight line between the two large black holes. Imagine this as a beaded necklace where they all barely touch. Does this cable stop the two large black holes suddenly and rapidly pull them together? Does the cable stretch, but stay connected, and slowly decelerate the large masses? If this is true then what happens if the thickness of the cable reaches something akin to Planck's length?

 

[PeterDonis]

Long ago I was told that if two black hole traveling rapidly relative to each other "brushed" past each other they'd pull each other in.

Can you give a reference?

Does this cable stop the two large black holes suddenly and rapidly pull them together?

It isn't a "cable". Black holes are not ordinary objects.

If I were you, I would drop all the extra small holes and just consider the two larger holes moving past each other. Obviously they will attract each other, so their paths will curve (in space--note that we are assuming we can model this situation as two holes moving in a "space" that does not change with time, which, since no exact solution is known in GR for this case, we can't actually demonstrate mathematically) towards each other. How much they will curve, and whether that will be enough for the holes to eventually merge into a single hole, will depend on the masses of the holes and how closely their paths approach each other.

 

[hexexpert]

Can you give a reference?

It isn't a "cable". Black holes are not ordinary objects.

If I were you, I would drop all the extra small holes and just consider the two larger holes moving past each other. Obviously they will attract each other, so their paths will curve (in space--note that we are assuming we can model this situation as two holes moving in a "space" that does not change with time, which, since no exact solution is known in GR for this case, we can't actually demonstrate mathematically) towards each other. How much they will curve, and whether that will be enough for the holes to eventually merge into a single hole, will depend on the masses of the holes and how closely their paths approach each other.

I can't find the old post from a couple of years back. I was exploring whether matter could escape a black hole if two black holes traveling near the speed of light barely touched. I interpreted the answer as either the black holes simple pass each other or if they reach some close proximity(?touch?) they'll merge. Apparently, there is no in-between of spewing off a shower of matter, or smallish black holes, as might happen with a glancing blow for normal matter. Nothing escapes a black hole, so once they touch, even if by a millimeter, it is over. Do the two black hole really screech to a halt, so to speak?

I used "cable" for a lack of a better term. Since the simple case seems counter intuitive to me I'm trying to create an even more extreme case. Two super massive black holes moving at relativistic speeds in opposite directions. Since matter can't escape a black hole then can a "thread/cable/neckless" of tiny black holes stop this juggernaut if they all touch? Even if the large black holes were light years apart?

 

[PeterDonis]

I was exploring whether matter could escape a black hole if two black holes traveling near the speed of light barely touched

It can't, because matter can't escape a black hole, period.

I interpreted the answer as either the black holes simple pass each other or if they reach some close proximity(?touch?) they'll merge. Apparently, there is no in-between of spewing off a shower of matter, or smallish black holes, as might happen with a glancing blow for normal matter.

That's correct.

Do the two black hole really screech to a halt, so to speak?

They will end up spiraling together and forming a single hole that is rotating very rapidly. At least, that's what I would expect a numerical simulation to show. Since, as I said before, we don't have an exact solution for this case, numerical simulation would be the only way to model it.

can a "thread/cable/neckless" of tiny black holes stop this juggernaut if they all touch?

The end result in this case would presumably be a single hole that would be rotating, but the exact axis of rotation would depend on the exact configuration of the holes that all came together.

 

[Ibix]

A planet is made up of lots of bits - atoms - which are spread out in space. In fact, the planet is defined by the volume its atoms occupy. A black hole, however, is a vacuum inside the event horizon - all infalling matter ends up in the singularity (or, at least, that's how GR models it). So two black holes "touching" isn't anything like two planets touching. It's more closely akin to two planets passing close enough to each other to end up in mutual orbit. The special thing about black holes is that there is some distance-of-closest-approach from which there is no way to escape the mutual orbit no matter how fast the holes are going.

 

[pervect]

I don't have a really good reference, but my understanding of the situation of two black holes traveling rapidly past each other is this:

The metric, or space-time geometry, (which terms I'm using interchangably hoping one of them makes some sense) of a ultra-relativisti black hole can be mathematically approximated by something called a "pp wave spacetime", <<link>>.

This is just an approximation, but if the velocity of the black holes is sufficiently close to "c" in what one might call the center-of-mass frame of the collision, it's a good approximation. One might make it exact by replacing the black holes with two pulses of ultra-energetic light, if one is so minded, in which case the pp wave is no longer an approximation, it's an exact description of the problem.

The pp wave isn't just a single point-like object, it has spatial extent. It might be best to regard it in this context as a field surrounding a black hole, if you can conceive of a field that's nothing more than geometry. Which, I should add, is not a bad way to think of General Relativity's description of a "gravitationl field". So one can think of the pp-wave as being the "gravitational field" of the two light pulses / black holes.

Solving the problem of such an interaction between two colliding pp waves is tricky. There is a fair amount of literature on the topic, but I'm not familiar with the details.

One of the possible outcomes of colliding pp waves is the formation of a singularity, a black hole. This means that if you have two colliding pp-waves, they can form a black hole, even if the light pulses or black holes which generate the pp-wave would be expected not to collide. (The expectation of them not colliding is based on thinking of the waves/black holes as propagating through a flat background space-time, rather than the actual curved space-time geometry that one gets when one gets when one does a full treatment of the problem according to General Relativity which includes the effects of gravity).

Another way of saying this - the "gravitational fields" of the two black holes or light pulses collide, even if the black holes or light pulses themselves don't.

Note that it's possible for two such colliding pp waves to form a black hole, but it's not guaranteed. When one tries to get to specifics, one runs into the interesting "hoop conjecure". This hasn't been proven AFAIK, but it gives a rule-of-thumb which purports to tell us when a black hole is formed by the collision, and when it isn't.

"Tensile strength" doesn't really enter into this in any meaningful way that I can think of. It's like asking "how strong is geometry".

 

[Jimmy]

Long ago I was told that if two black hole traveling rapidly relative to each other "brushed" past each other they'd pull each other in. I find it odd that a massive object traveling near the speed of light would suddenly stop dead in its track.

Can you give a reference?

I believe this is the thread:
Can you scoop out part of a black hole?

 

[Dale]

Apparently, there is no in-between of spewing off a shower of matter, or smallish black holes, as might happen with a glancing blow for normal matter.

They will throw off a lot of gravitational waves as they spiral in.