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  • On Wednesday April 10th 2019 you will probably see the first-ever image of a

  • black hole. That's when the Event Horizon Telescope will be releasing their

  • results and I haven't seen them yet but I think they're going to look something

  • like this and I can be relatively confident because well it's gonna look a

  • bit like a fuzzy coffee mug stain. But if you are disappointed by this image I

  • think that misses the gravity of the situation. From this image we should be

  • able to tell whether the general theory of relativity accurately predicts what

  • happens in the strong gravity regime that is what happens around a black hole

  • what I want to do here is understand what exactly we are seeing in this image

  • so here is my mock black hole of science and this sphere represents the event

  • horizon. That is the location from which not even light fired radially away from

  • the black hole could be detected by an outside observer. All of the world lines

  • end up in the center of the black hole in the singularity once you're inside

  • here there is no coming back not even for light. The radius of the

  • event horizon is known as the Schwarzschild radius. Now if we were just

  • to look at a black hole with nothing around it we would not be able to make

  • an image like this because well it would just absorb all electromagnetic

  • radiation that falls on it but the black hole that they're looking at

  • specifically the one in the center of our Milky Way galaxy, Sagittarius A*

  • has matter around it in an accretion disk. In this accretion disk there is

  • dust and gas swirling around here very chaotically it's incredibly hot we're

  • talking to millions of degrees and it's going really fast a significant fraction

  • of the speed of light and it's this matter that the black hole feeds off and

  • gets bigger and bigger over time but you'll notice that the accretion disk

  • does not extend all the way in to the event horizon. Why is that? Well that's

  • because there is an inner most stable circular orbit and for matter around a

  • non-spinning black hole that orbit is at three Schwarzschild

  • radii now in all likelihood the black hole at the center of our galaxy will be

  • spinning but for simplicity I'm just considering the non spinning case. You

  • can see my video on spinning black holes if you want to find out more about

  • that. So this is the innermost orbit for matter going around the black hole if it

  • goes inside this orbit it very quickly goes into the center of the black hole

  • and we never hear from it again but there is something that can orbit closer

  • to the black hole and that is light because light has no mass it can

  • actually orbit at 1.5 Schwarzschild radii. Now here i'm representing it with a ring

  • but really this could be in any orientation so it's a sphere of photon

  • orbits and if you were standing there of course you could never go there but if

  • you could you could look forward and actually see the back of your head

  • because the photons could go around and complete that orbit. Now the photon

  • sphere is an unstable orbit meaning eventually either the photons have to

  • spiral into the singularity or spiral out and head off to infinity now the

  • question I want to answer is what does this black quote-unquote shadow in the

  • image correspond to in this picture of what's actually going on around the

  • black hole. Is it the event horizon? Are we simply looking at this? or is it the

  • photon sphere? or the inner most stable circular orbit? Well things are

  • complicated and the reason is this black hole warps space-time around it which

  • changes the path of light rays so they don't just go in straight lines like we

  • normally imagine that they do I mean they are going in straight lines but

  • space-time is curved so yeah they go in curves so the best way to think of this

  • is maybe to imagine parallel light rays coming in from the observer and striking

  • this geometry here. Of course if the parallel light rays cross the event

  • horizon we'll never see them again so they're gone that will definitely be a

  • dark region but if a light ray comes in just above the event

  • Rison it too will get bent and end up crossing the event horizon it ends up in

  • the black hole. Even a light ray coming in the same distance away as the photon

  • sphere will end up getting warped into the black hole and curving across the

  • event horizon so in order for you to get a parallel ray which does not end up in

  • the black hole you actually have to go out 2.6 radii away if a light ray comes

  • in 2.6 Schwarzschild radii away it will just graze the photon sphere at its

  • closest approach and then it will go off to infinity and so the resulting shadow

  • that we get looks like this it is 2.6 times bigger than the event horizon. You

  • say what are we really looking at here? what is this shadow? well in the center

  • of it is the event horizon. It maps pretty cleanly onto onto the center of

  • this shadow but if you think about it light rays going above or below also end

  • up crossing the event horizon just on the backside. So in fact what we get is

  • the whole back side of the event horizon mapped onto a ring on this shadow. So

  • looking from our one point in space at the black hole we actually get to see

  • the entirety of the black hole's event horizon. I mean maybe it's silly to talk

  • about seeing it because it's completely black but that really is where the

  • points would map to on this shadow. It gets weirder than that

  • because the light can come in and go around the back and say get absorbed in

  • the front you get another image of the entire horizon next to that and another

  • annular ring and then another one after that and another one after that and you

  • get basically infinite images of the event horizon as you approach the edge

  • of this shadow. So what is the first light that we can see? It is those light

  • rays that come in at just such an angle that they graze the photon sphere and

  • then end up at our telescopes. And they produce a shadow which is 2.6 times the

  • size of the event horizon. So this is roughly what we'd see if we happen to be

  • looking perpendicular to the accretion disk but more likely we will be looking

  • at some sort of random angle to the accretion disk. We may be even looking edge-on

  • And in that case do we see this shadow of the black hole? you might think

  • that we wouldn't but the truth is because of the way the black hole warps

  • space-time and bends light rays, we actually see the back of the accretion

  • disk the way it works is light rays coming off the accretion disk bend over

  • the top and end up coming to our telescopes so what we end up seeing is

  • something that looks like that. Similarly light from the bottom of the

  • accretion disk comes underneath gets bent underneath the black hole and comes

  • towards us like that and this is where we get an image that looks something

  • like the interstellar black hole.

  • it gets even crazier than this because light

  • that comes off the top of the accretion disk here can go around the back of the

  • black hole graze the photon sphere and come at the bottom right here producing

  • a very thin ring underneath the shadow. Similarly light from underneath the

  • accretion disk in the front can go underneath and around the back and come

  • out over the top which is why we see this ring of light here. This is what we

  • could see if we were very close to the black hole, something that looks truly

  • spectacular. One other really important effect to consider is that the matter in

  • this accretion disk is going very fast, close to the speed of light and so if

  • it's coming towards us it's gonna look much brighter than if

  • it's going away. That's called relativistic beaming or Doppler beaming

  • and so one side of this accretion disk is going to look much brighter than the

  • other and that's why we're gonna see a bright spot in our image. So hopefully

  • this gives you an idea of what we're really looking at when we look at an

  • image of a black hole if you have any questions about any of this please leave

  • them in the comments below and I will likely be making a video for the launch

  • of the first ever image of a black hole so I'll try to answer them then. Until

  • then I hope you get as much enjoyment out of this as I have

  • because this has truly been my obsession for like the last week.

  • I guess what

  • would be exciting is to watch it over time how it changes, right? there's a lot of

  • hope that there are blobs moving around and you know if you see a blob going

  • round the front and then it goes around the back but you see it in the back

  • image etc then that's gonna be kind of cool

On Wednesday April 10th 2019 you will probably see the first-ever image of a

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B1 中級

ブラックホールのイメージを理解する方法 (How to Understand the Black Hole Image)

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    林宜悉 に公開 2021 年 01 月 14 日
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