Author Topic: Black holes and the speed of light  (Read 3408 times)

Offline Grawk1

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Black holes and the speed of light
« on: October 09, 2013, 08:59:07 AM »
I'm tutoring a very curious student who is interested in physics, and he has a question which I promised I would ask to a real physicist.

He wants to know whether an object falling into a black hole could ever go faster than the speed of light.

I have no idea how to answer this; I presume the answer is no, but I can't figure out why this would be the case. I know that objects approaching the speed of light become more massive, but surely a black hole would have an infinite escape velocity, having no minimum radius?

Offline bobmath

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Re: Black holes and the speed of light
« Reply #1 on: October 09, 2013, 11:28:47 AM »
Have you listened to Ben's show on falling into a black hole? Paradoxically, a thing that falls into a black hole appears to move very slowly... depending on your point of view. Anyway, the escape velocity doesn't need to be infinite, it just has to be enough to keep light from escaping.

I live about a mile down the road from CSU Fullerton, where Dr. Read teaches. Her office is in a room that used to be a lab I worked in. Maybe I should stop by and say hi sometime, but I wouldn't want to be weird.

Offline bobmath

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Re: Black holes and the speed of light
« Reply #2 on: October 09, 2013, 02:50:45 PM »
I've been thinking a little bit more about where you're going with this. Two point masses gravitationally attracting each other gain "infinite" kinetic energy as they get closer together, and thus infinite velocity, under Newtonian mechanics. But in special relativity, infinite kinetic energy only accelerates you up to the speed of light, not any faster. Also, the object falling into the black hole isn't really a point mass. Refer to the "spaghettification" discussion in the podcast.
« Last Edit: October 09, 2013, 02:53:06 PM by bobmath »

Offline Grawk1

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Re: Black holes and the speed of light
« Reply #3 on: October 09, 2013, 05:24:03 PM »
Okay, I see what you mean (and I have listened to the falling into a black hole show, but I didn't find any answer to this specific question)

But if kinetic energy approaches infinity as any massive object approached the point of singularity, doesn't that mean that the mass is infinite for an infinitesimal period of time? Even after spaghettification, wouldn't even a quark momentarily become so heavy as to make the black hole the most massive thing in the universe?

Offline bobmath

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Re: Black holes and the speed of light
« Reply #4 on: October 09, 2013, 07:47:34 PM »
Speaking Newtonially, the "infinite kinetic energy" is balanced by "negative infinite potential energy." I'm not sure how that plays out in general rel.

And I don't think anyone knows exactly what happens when a quark hits a gravitational singularity, but it's a good question.

Offline Grawk1

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Re: Black holes and the speed of light
« Reply #5 on: October 09, 2013, 09:17:15 PM »
Okay, so to clarify: I drop a stone into a black hole, it gets spaghettified into a stream of subatomic particles, as they accelerate they approach the speed of light, but get more and more massive as they get closer. At some point in this journey, they cross the event horizon and become forever inaccessible to the rest of the universe and become part of the black hole.

Also, all the awesome time-bending stuff that was in that Ty-Phy episode happens, with the dopplering timeshadows.

Have I got this right?

Offline bn

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Re: Black holes and the speed of light
« Reply #6 on: October 09, 2013, 10:18:44 PM »
Hi!

hi.
okay so. I'm afraid that a lot of the ideas that I hear you talking about are kind of not... pertinent to falling into a black hole.

Quote
He wants to know whether an object falling into a black hole could ever go faster than the speed of light.

So the "faster than the speed of light" law is kind of from non-curved spacetime. when spacetime is curved all you can say is "the stuff near you can't move faster than the speed of light".

because when you deal with stuff that's far away from you in a curved spacetime, everything gets mucky... spacetime itself starts flowing.

so one way to describe the uniform expansion of the universe says that volume keeps bubbling into existence (causing the expansion), and so the "distance" between us and an object really-really-super-far away can increase "faster" than the speed of light.

anyway, when something falls into a black hole, it doesn't really feel itself accelerate. it feels weightless the whole time, until it hits the singularity. So it's not really "accelerating", exactly. instead, the distance between US (outside) and them (falling in) is increasing at an increasing rate.
 
in this sense, once it crosses the event horizon of a black hole, it is moving away from us faster than the speed of light.

HAHAHA. relativity is full of riddles!


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Offline bn

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Re: Black holes and the speed of light
« Reply #7 on: October 09, 2013, 10:24:32 PM »
But if kinetic energy approaches infinity as any massive object approached the point of singularity, doesn't that mean that the mass is infinite for an infinitesimal period of time? Even after spaghettification, wouldn't even a quark momentarily become so heavy as to make the black hole the most massive thing in the universe?

yeah okay. so this stuff isn't really relevant to normal schwazschild black holes. because there's nothing at the singularity. it's singular. it's the edge of the universe.
once something falls into a (schwazschild) black hole, it won't really hit anything that isn't also falling into the middle.

but there IS a different type of black hole. (several different such types, actually) where everyone doesn't end up getting pushed into the singularity. Instead, there's like... a region inside the black hole where things aren't so squishy.
um. I like to think of the "inescapable" region of a black hole as, like, a waterslide. once you're on it, you can't climb back out.
but in these black holes, there's a region in the middle... like the pool at the bottom of the waterslide.

okay, so... what happens if you hang out where the pool meets the black hole? you get hit with infalling stuff REALLY HARD.

and inside a black hole, if you cuddle up to the waterslide part, you get SMACKED WITH STUFF. and the collision is INFINITELY POWERFUL! so much so that the inside of the black hole is considered "unstable". and the effect of getting hit by stuff infinitely hard is called "mass inflation".

hahahahaha! RELATIVITY!


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Offline bobmath

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Re: Black holes and the speed of light
« Reply #8 on: October 10, 2013, 08:16:59 AM »
okay so. I'm afraid that a lot of the ideas that I hear you talking about are kind of not... pertinent to falling into a black hole.
Yeah, I kind of got... sucked in. Thanks for speaking up. I hadn't heard of mass inflation as a real thing before.

Offline bn

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Re: Black holes and the speed of light
« Reply #9 on: October 10, 2013, 01:46:48 PM »
well. mass inflation is weird.
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Offline Grawk1

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Re: Black holes and the speed of light
« Reply #10 on: October 11, 2013, 07:36:59 PM »
Thanks for clarifying that - you're the best at this stuff, Ben!

When you say mass inflation, is that the gravitational potential energy lost by falling into the black hole being converted into mass? Does this happen at all with matter falling into non-singularity gravity wells (like the Earth?)

Offline bn

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Re: Black holes and the speed of light
« Reply #11 on: October 11, 2013, 09:27:13 PM »
I think it's called "mass inflation" for poetic reasons.
it's more formally referred to as an instability associated with the inner cauchy horizon of the black hole.

pretty much, it goes like this. people do simulations assuming that *small* amounts of matter bumping around won't deform the spacetime geometry too much (like, assuming that when you roll a marble across a trampoline, it doesn't bend the surface too much).

but then it turns out that in these circumstances, the geometry should get deformed A WHOLE LOT. at this point in time, people throw up their hands and go "well, crap."

the stuff that falls into a black hole has its mass added to the black hole's mass when it crosses the horizon. mass inflation occurs well within the horizon, and has no real effect on how the outside universe observes a black hole.

and as for it happening when anything falls in a non-singular gravity well... sometimes books fall down from high up and hit me in the head. and that hurts? maybe i don't understand the question.
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