1 00:00:00,000 --> 00:00:05,437 And now, finally, armed with all of the understanding that we could gear 2 00:00:05,437 --> 00:00:10,173 ourselves up with, the general theory of relativity were going to try to talk 3 00:00:10,173 --> 00:00:15,090 about what might happen to the core of a star that is too massive to be stabilized 4 00:00:15,090 --> 00:00:17,831 by neutron degeneracy, and collapses completely. 5 00:00:17,831 --> 00:00:22,263 And then, there, as far as we know, is nothing to stop the collapse, and, the 6 00:00:22,263 --> 00:00:26,171 star collapses completely. We won't talk much about what happens to 7 00:00:26,171 --> 00:00:29,670 the star, but we'll talk about what happens outside the star. 8 00:00:29,670 --> 00:00:34,277 The collapse itself is, of course, a very highly turbulent and energetic process 9 00:00:34,277 --> 00:00:38,709 releasing tons of, gravitational potential energy, and creating a wild and 10 00:00:38,709 --> 00:00:42,850 violent and turbulent supernova. There are people who model such things. 11 00:00:42,850 --> 00:00:47,815 We will not, discuss what they find. We will discuss what's left behind 12 00:00:47,815 --> 00:00:51,284 outside the star. And we'll start this a little bit 13 00:00:51,284 --> 00:00:55,025 obliquely by talking about our gravitational red shift. 14 00:00:55,025 --> 00:00:57,949 Remember, from the principle of equivalence, 15 00:00:57,949 --> 00:01:02,167 we found that, near Earth, if you shoot light up at height h, 16 00:01:02,167 --> 00:01:05,703 you find a gravitational red shift given by gh over c2. 17 00:01:05,703 --> 00:01:08,364 squared. This has to do with the con, the 18 00:01:08,364 --> 00:01:12,846 acceleration of gravity being G. We've already, played with that game 19 00:01:12,846 --> 00:01:14,551 before. And away from Earth, 20 00:01:14,551 --> 00:01:19,222 we expect that, because the force of gravity is weaker as you move farther 21 00:01:19,222 --> 00:01:23,956 away. If you're not near the earth's surface, we expect GH to be replaced by 22 00:01:23,956 --> 00:01:26,670 something like minus GM over R up to a constant. 23 00:01:26,670 --> 00:01:30,458 And, in fact, you can do the general relativistic calculation. 24 00:01:30,458 --> 00:01:34,940 And you find that if you're observing from a great distance from Earth. 25 00:01:34,940 --> 00:01:40,972 And way off in infinity, and someone is emitting light at distance R from earth. 26 00:01:40,972 --> 00:01:44,136 So the situation is that here is the earth, 27 00:01:44,136 --> 00:01:49,840 you are sitting a distance R from earth emitting a light beam and is traveling 28 00:01:49,840 --> 00:01:54,764 off, and this light is being received way far off from earth essentially at 29 00:01:54,764 --> 00:01:58,440 infinite distance. Then it will be reddened because your 30 00:01:58,440 --> 00:02:03,561 emitting from the ground floor from the top floor, but the amount is not GH of 31 00:02:03,561 --> 00:02:06,122 course. there is the weakening of the 32 00:02:06,122 --> 00:02:11,510 gravitational field the correct relativistic expression, is this one. 33 00:02:11,510 --> 00:02:17,454 The observed frequency will be the emitted frequency divided by the square 34 00:02:17,454 --> 00:02:23,477 root of this ratio. we can use the Newton, Newton's approxiamation to write 35 00:02:23,477 --> 00:02:29,103 this as lambda zero, times 1 minus 2GN over RC squared to the minus a half and 36 00:02:29,103 --> 00:02:35,748 then, That's the same as lambda zero times one minus times two times minus a 37 00:02:35,748 --> 00:02:42,173 half is plus, GM over r c squared and that's the expression I wrote there. 38 00:02:42,173 --> 00:02:45,496 And so, to a good approximation, we get exactly 39 00:02:45,496 --> 00:02:49,382 what we expected. Here is the GM over R that we expected. 40 00:02:49,382 --> 00:02:55,003 This is valid so long as this expression here in the square root is much smaller 41 00:02:55,003 --> 00:02:58,264 than one. This means that R needs to big, bigger 42 00:02:58,264 --> 00:03:01,803 than what? Well, such that 2GM over RC squared is 43 00:03:01,803 --> 00:03:05,897 much less than 1or R is much bigger than GM over C squared. 44 00:03:05,897 --> 00:03:10,686 This is called Schwarzschild radius, and for Earth the Schwarzschild radius 45 00:03:10,686 --> 00:03:13,092 plugging in, and earth over here is about nine 46 00:03:13,092 --> 00:03:15,710 millimeters. You're not likely to be broadcasting from 47 00:03:15,710 --> 00:03:19,487 less than nine millimeters from the center of earth, so I'm not worried about 48 00:03:19,487 --> 00:03:24,277 that too much in the case of earth. But what happens if R is not much bigger 49 00:03:24,277 --> 00:03:29,150 than the Schwarzschild radius. Then this redshift factor can become 50 00:03:29,150 --> 00:03:34,909 quite significant and it's deviation from the Newton approximation can be big. 51 00:03:34,909 --> 00:03:40,815 because the X here is not less than one. And in fact, when you get near to not, 52 00:03:40,815 --> 00:03:46,279 the, the, Schwarzschild radius for some given mass what happens is that this 53 00:03:46,279 --> 00:03:50,340 denominator vanishes and the redshift becomes infinite. 54 00:03:50,340 --> 00:03:54,431 So can you even do such a thing? Well the Schwarzschild radius for earth 55 00:03:54,431 --> 00:03:58,863 is nine millimeters, you can't get there. You need something where mass is more 56 00:03:58,863 --> 00:04:02,670 compactly concentrated. if you take the Schwarzschild radius for 57 00:04:02,670 --> 00:04:06,591 any object you can compute, it's directly proportional to the mass. 58 00:04:06,591 --> 00:04:10,739 And it can compute the schwartzfield radius for the sun to be about three 59 00:04:10,739 --> 00:04:13,751 kilometers. So the Schwarzschild radius for an object 60 00:04:13,751 --> 00:04:18,297 of solar mass is three kilometers, the Schwarzschild radius for an object of ten 61 00:04:18,297 --> 00:04:22,852 solar masses is 30 kilometers and so on. Neutron stars remember have a mass of 62 00:04:22,852 --> 00:04:26,816 about one and a half solar masses, and their radii are ten kilometers, so 63 00:04:26,816 --> 00:04:30,539 they're not too far from the Schwarzschild limit you can get to 64 00:04:30,539 --> 00:04:33,589 within, Three, maybe four Schwarzschild radii of 65 00:04:33,589 --> 00:04:36,809 a neutron star. At that point, when light is being 66 00:04:36,809 --> 00:04:41,870 emitted from the surface of a neutron star, the gravitational redshift due to 67 00:04:41,870 --> 00:04:46,931 GR effect is very significant. So neutron stars are pretty close to the 68 00:04:46,931 --> 00:04:50,349 Schwarzs, to be inside their own Schwarzschild limit. 69 00:04:50,349 --> 00:04:55,212 But if you can imagine an object that collapses to its even denser than a 70 00:04:55,212 --> 00:05:00,339 neutron star, then there will be a point in space, a ball around this object of 71 00:05:00,339 --> 00:05:06,680 radius determined by its mass, this Schwarzschild radius and when, you 72 00:05:06,680 --> 00:05:11,290 approach that distance from the center of the object, 73 00:05:11,290 --> 00:05:14,554 the gravitational redshift diverges and becomes infinite. 74 00:05:14,554 --> 00:05:18,460 What does this mean? This means that if I'm watching from very 75 00:05:18,460 --> 00:05:23,585 far away and, and watching something fall onto this massive, dense object, which 76 00:05:23,585 --> 00:05:28,448 I'm going to call a black hole. then when I look at it from afar, I will 77 00:05:28,448 --> 00:05:32,982 never see the thing that I'm watching getting there because, remember, 78 00:05:32,982 --> 00:05:36,334 gravitational redshift is really time slowing down. 79 00:05:36,334 --> 00:05:41,328 As I see, as I observe from far away, something falling onto a, the black, a 80 00:05:41,328 --> 00:05:46,352 black hole or a black hole's horizon, this ball around the massive compact 81 00:05:46,352 --> 00:05:51,326 object who's radius is the Schwarzschild radius is called the horizon for reasons 82 00:05:51,326 --> 00:05:55,329 that will become apparent. But as something approaches the horizon, 83 00:05:55,329 --> 00:06:00,362 if you're observing it from far away what you're going to observe is that it slows 84 00:06:00,362 --> 00:06:04,487 down and never gets there. It basically freezes as it approaches the 85 00:06:04,487 --> 00:06:07,458 horizon. Moreover any light, when I say you see it 86 00:06:07,458 --> 00:06:10,370 you would be seeing it by light say as a bright. 87 00:06:10,370 --> 00:06:14,895 luminous object, its light will be redshifted in the amount of energy per 88 00:06:14,895 --> 00:06:19,540 photon, remember, is proportional to the frequency so decreases with increasing 89 00:06:19,540 --> 00:06:22,636 wavelength. There's less energy in a red photon than 90 00:06:22,636 --> 00:06:26,447 there is in a blue photon. So the amount of energy this thing is 91 00:06:26,447 --> 00:06:31,270 emitting becomes less and less what you would see as this object slowed down and 92 00:06:31,270 --> 00:06:36,153 dimmed and then it will basically become dark as it approached the horizon, but it 93 00:06:36,153 --> 00:06:40,738 would take an infinite num, amount of time as you see it from far away for 94 00:06:40,738 --> 00:06:45,556 something to actually get to the horizon. In particular since any light is coming 95 00:06:45,556 --> 00:06:48,110 from the horizon is infinitely red shifted. 96 00:06:48,110 --> 00:06:52,691 That means it carries zero energy. No light comes out from this ball of 97 00:06:52,691 --> 00:06:57,884 radius Schwarzschild radius around whatever this compact massive object is. 98 00:06:57,884 --> 00:07:03,008 This is why we call it a black hole, because absolutely no light can leave. 99 00:07:03,008 --> 00:07:06,055 There's this area, region called the horizon. 100 00:07:06,055 --> 00:07:09,032 It's a ball of radius Schwarzschild radius. 101 00:07:09,032 --> 00:07:14,225 Any light from that ball or within it, but from that, sphere, no light can 102 00:07:14,225 --> 00:07:17,298 emerge. And so of course not from the inside now 103 00:07:17,298 --> 00:07:21,770 because of the way gravitational redshifts work light that is falling on 104 00:07:21,770 --> 00:07:26,654 to the horizon is blue shifted so if you happen to be sitting near the horizon you 105 00:07:26,654 --> 00:07:29,420 can look back and light falling on you will be. 106 00:07:29,420 --> 00:07:34,655 Intensely blue shifted and time will appear to you to be moving faster so your 107 00:07:34,655 --> 00:07:39,444 clock will run slow, you can look back and watch you know, the end of the 108 00:07:39,444 --> 00:07:43,849 universe happening behind you as you are sitting near the horizon. 109 00:07:43,849 --> 00:07:49,276 It will take a mere instance of your time because of this general relativistic red 110 00:07:49,276 --> 00:07:52,403 shift. this is what the horizon is the horizon 111 00:07:52,403 --> 00:07:57,699 of a black hole is the point at which the gravitational red shift is infinite this 112 00:07:57,699 --> 00:08:02,293 is why it is that no light comes out this requires an extremely intense 113 00:08:02,293 --> 00:08:05,628 gravitational field. typically we observe things from 114 00:08:05,628 --> 00:08:08,315 infinity. Notice that when I say you have to be 115 00:08:08,315 --> 00:08:12,775 infinite far away, the gravitational redshift will be infinite compared to any 116 00:08:12,775 --> 00:08:15,920 finite distance. All the infinity is coming out and the 117 00:08:15,920 --> 00:08:21,152 region where R is very close to RS. So if you're out at five Schwarzschild 118 00:08:21,152 --> 00:08:26,872 radii, you will still see someone, at the Schwarzschild radius have an infinite, 119 00:08:26,872 --> 00:08:28,965 red shift. So things slow down. 120 00:08:28,965 --> 00:08:33,150 Nothing ever goes through a hurr-, a black hole's horizon. 121 00:08:33,150 --> 00:08:37,057 So, if you ask what happened to the star as it collapsed. 122 00:08:37,057 --> 00:08:41,806 The answer is, I never saw that. In as well see it very far from the star 123 00:08:41,806 --> 00:08:46,979 the stars collapse stopped and froze and dimmed and darkened and all we see is no 124 00:08:46,979 --> 00:08:51,836 more starlight coming from there we'll see later what the other astronomical 125 00:08:51,836 --> 00:08:56,000 signatures are but we've never actually observed let alone see 126 00:08:56,000 --> 00:08:59,855 Star collapse into a black hole for the simple reason that by our clocks, it 127 00:08:59,855 --> 00:09:02,590 hasn't happened yet. It takes an infinite amount of time. 128 00:09:02,590 --> 00:09:08,250 Now okay that's looking from far away what happens if you get more, close to a 129 00:09:08,250 --> 00:09:13,630 black hole, then you can see some interesting effects as you get to within 130 00:09:13,630 --> 00:09:19,011 a few Schwarzschild radii relativistic effects become interesting so stable 131 00:09:19,011 --> 00:09:22,713 orbits exist. you can draw nice, stable circular orbits 132 00:09:22,713 --> 00:09:27,156 around an object like the sun, and as you get closer, to a black hole, 133 00:09:27,156 --> 00:09:29,886 relativistic effects become more important. 134 00:09:29,886 --> 00:09:32,679 You have to orbit rather fast. And, for radii, 135 00:09:32,679 --> 00:09:35,599 less than three times this Schwarzschild radius, 136 00:09:35,599 --> 00:09:39,580 No stable orbits exist. there exist circular orbits inside that 137 00:09:39,580 --> 00:09:43,156 radius, but they're all unstable. What this implies is that, 138 00:09:43,156 --> 00:09:47,436 any small perturbation, rather than knocking you into an elliptical orbit, 139 00:09:47,436 --> 00:09:52,126 will knock you into an orbit that either falls into the black hole or away from 140 00:09:52,126 --> 00:09:55,292 the black hole. So, that means that when we are looking 141 00:09:55,292 --> 00:09:57,520 at objects orbiting a black hole. None. 142 00:09:57,520 --> 00:10:02,277 Because there's always a britter basion from somewhere none will be orbiting near 143 00:10:02,277 --> 00:10:06,977 than three svoutshield radieye from the black hole now if the black hole has the 144 00:10:06,977 --> 00:10:11,386 mass of a few solar masses that's ten kilometers out that's not really very 145 00:10:11,386 --> 00:10:15,912 impressive but if a black hole has could stand the mass of 1,000 solar masses 146 00:10:15,912 --> 00:10:19,857 that's 3,000 kilometers will be the closest that anything can orbit. 147 00:10:19,857 --> 00:10:23,079 And by that time maybe you can make some hay of it. 148 00:10:23,079 --> 00:10:28,086 because of the deflection of light, at a radius, you can compute of one and a half 149 00:10:28,086 --> 00:10:30,821 times the solar ray, the, the, Schwarzschild radius. 150 00:10:30,821 --> 00:10:35,280 You find what's called the photosphere. There, light can actually orbit in a 151 00:10:35,280 --> 00:10:38,967 closed, circular orbit. Light is deflected by this massive star. 152 00:10:38,967 --> 00:10:43,129 It's deflected enough that you can imagine photons running in circles, 153 00:10:43,129 --> 00:10:46,586 around at the speed of light, around this massive object. 154 00:10:46,586 --> 00:10:51,195 Unfortunately, they don't stay there. That orbit is unstable, but what it means 155 00:10:51,195 --> 00:10:55,803 is that by the time you get to within one and a half Schwarzschild radii, the 156 00:10:55,803 --> 00:11:00,531 lensing, the optical effects of the black hole are going to be very extreme, and 157 00:11:00,531 --> 00:11:04,721 even farther out they are quite marked and we'll see it back in a bit. 158 00:11:04,721 --> 00:11:06,819 And the other thing, of course, is that 159 00:11:06,819 --> 00:11:10,029 because, so what is the deal? Why is gravity so intense in a black 160 00:11:10,029 --> 00:11:12,350 hole? It's got nothing to do with the fact that 161 00:11:12,350 --> 00:11:14,720 it collapsed. It, gravity is intense for the same 162 00:11:14,720 --> 00:11:17,980 reason gravitation of a one solar mass neutron star is so intense. 163 00:11:17,980 --> 00:11:23,172 It's because you can get so close. It's the GM over R squared becoming huge 164 00:11:23,172 --> 00:11:26,565 when N is the solar mass, but R is ten kilometers. 165 00:11:26,565 --> 00:11:31,342 In this case there is an, general relativistic enhancement, and in the 166 00:11:31,342 --> 00:11:35,774 neutron star case by the way. Similarly, the M over R cubed tidal 167 00:11:35,774 --> 00:11:40,482 forces become huge because you can get so near to such a large mass. 168 00:11:40,482 --> 00:11:45,649 And so, tidal forces can become extreme when you get so close to, when you get 169 00:11:45,649 --> 00:11:49,514 close to a black hole. However, I note that since the closest 170 00:11:49,514 --> 00:11:54,216 you're ever going to get is the Schwarzschild radius, and if your size is 171 00:11:54,216 --> 00:11:59,112 D, this is our estimate for the tidal acceleration between, say, your head and 172 00:11:59,112 --> 00:12:02,139 your feet. You can stick for D, I don't know, two 173 00:12:02,139 --> 00:12:07,100 meters if you're a tall person. it's twice g times the mass divided by 174 00:12:07,100 --> 00:12:11,898 whatever your distance is cubed, we'll plug it in as the distance the 175 00:12:11,898 --> 00:12:17,447 Schwarzschild radius. The Schwarzschild radius, remember, RS, is, 2GM over C 176 00:12:17,447 --> 00:12:23,670 squared, and so plugging R cubed here, we see that one G and one M and one two 177 00:12:23,670 --> 00:12:30,217 cancel, leaving us with four G squared M squared on the denominator, and a D times 178 00:12:30,217 --> 00:12:34,420 C to the 6th on top. These accelerations can be huge, 179 00:12:34,420 --> 00:12:39,377 but because, the larger, the more massive the black hole, the less extreme the 180 00:12:39,377 --> 00:12:42,639 tidal effects are. So a solar mass black hole will 181 00:12:42,639 --> 00:12:47,270 completely rip you to sheds if you approach its horizon. A four billion 182 00:12:47,270 --> 00:12:51,836 solar mass black hole will not. In fact, you might not even notice that 183 00:12:51,836 --> 00:12:55,620 you crossed the horizon. We'll talk about that in a second. 184 00:12:55,620 --> 00:13:00,775 Okay so this is what you'd see, a few Schwarzschild radii, I want to go and 185 00:13:00,775 --> 00:13:05,653 look at the horizon and beyond it, How can I see beyond the horizon? 186 00:13:05,653 --> 00:13:10,808 I thought you could never get there? Well no, no, you can never get there, as 187 00:13:10,808 --> 00:13:16,243 seen by a clock, ticking far away here on earth, but if you were to fall into a 188 00:13:16,243 --> 00:13:18,874 black hole, believe me, you would fall in. 189 00:13:18,874 --> 00:13:23,181 I never said the star never collapsed. I said we have never seen it. 190 00:13:23,181 --> 00:13:28,644 It hasn't happened in our time. This is the weirdness of gravitational, 191 00:13:28,644 --> 00:13:32,051 redshifts. the star, if you were near the star, you 192 00:13:32,051 --> 00:13:36,101 would have been collapsed. The star itself indeed collapsed, and 193 00:13:36,101 --> 00:13:40,578 we'll see what happened to it, but, We, from far away, have not seen it. 194 00:13:40,578 --> 00:13:45,455 So what we need if we want to, study things closer into the black hole is we 195 00:13:45,455 --> 00:13:49,591 need to use a better clock. Let's use the clock of an observer that 196 00:13:49,591 --> 00:13:53,480 is freely falling in. And then the shape that you see of the, 197 00:13:53,480 --> 00:13:58,172 neighborhood or vicinity of the black hole is given by this sort of diagram 198 00:13:58,172 --> 00:14:01,752 here to the right. And I have to elaborate a little bit on 199 00:14:01,752 --> 00:14:04,654 what this diagram means. So these, this diagonal, 200 00:14:04,654 --> 00:14:09,000 this region over here is, the space outside the black hole, 201 00:14:09,000 --> 00:14:13,211 and out here, very far away, is where we are. 202 00:14:13,211 --> 00:14:21,144 now, this line over here, this thing over here, and this thing over here, this is 203 00:14:21,144 --> 00:14:25,058 the horizon. Now, it's very strange, this is a space 204 00:14:25,058 --> 00:14:28,522 time diagram. This is the radial direction and this is 205 00:14:28,522 --> 00:14:32,372 the time direction. And what you notice we've ignored the 206 00:14:32,372 --> 00:14:37,505 fact that you can go around a black hole, we've pretended only distance from the 207 00:14:37,505 --> 00:14:42,060 black hole and time, are relevant. And what you notice here is something 208 00:14:42,060 --> 00:14:45,461 very strange. The horizon is not a place at all, it is 209 00:14:45,461 --> 00:14:49,310 tilted at 45 degrees. The horizon is the position of a light 210 00:14:49,310 --> 00:14:53,801 beam, when you use suitable coordinates to be able to distinguish that. 211 00:14:53,801 --> 00:14:58,535 In the coordinates we got using clocks from far away, you couldn't really tell 212 00:14:58,535 --> 00:15:02,780 that because the light cones in those coordinates were squished down to 213 00:15:02,780 --> 00:15:05,551 nothing. But in these coordinates where you can 214 00:15:05,551 --> 00:15:10,385 see what's going on near the horizon, you see that the horizon is in fact, could be 215 00:15:10,385 --> 00:15:14,570 the world line of a light beam. And this immediately explains why light 216 00:15:14,570 --> 00:15:15,750 cannot leave. So, 217 00:15:15,750 --> 00:15:20,715 if you are an observer near the horizon, you can still broadcast a signal, and it 218 00:15:20,715 --> 00:15:25,494 will at some point arrive far away, but once you cross the horizon, and you're 219 00:15:25,494 --> 00:15:30,397 inside, a signal even traveling at the speed of light, will never get out of the 220 00:15:30,397 --> 00:15:32,507 horizon. To get out of the horizon, a signal would 221 00:15:32,507 --> 00:15:35,424 have to, would have to travel faster than light. 222 00:15:35,424 --> 00:15:39,893 And that is why, no kind of proportion will get you out, once you cross a 223 00:15:39,893 --> 00:15:44,423 blackhole's horizon. And this is very strange, because we said the horizon was 224 00:15:44,423 --> 00:15:48,085 a place, but suddenly it appears to be a light-like thing. 225 00:15:48,085 --> 00:15:50,808 It's a, it's different places at different times. 226 00:15:50,808 --> 00:15:56,952 How did the horizons move with time? this again has to do with the fact that 227 00:15:56,952 --> 00:16:01,863 it moves as seen by a clock that is relevant near the horizon. 228 00:16:01,863 --> 00:16:06,059 Remember, this clock ticks infinitely slowly, as seen from far away. 229 00:16:06,059 --> 00:16:09,111 So from far away, the horizon looks like a place. 230 00:16:09,111 --> 00:16:13,434 This is a more accurate description. This is why light cannot escape. 231 00:16:13,434 --> 00:16:17,121 Over here is the interior. This is where the black hole is. 232 00:16:17,121 --> 00:16:21,878 And if you try to relate, this description, for the description in terms 233 00:16:21,878 --> 00:16:26,676 of distance from the black hole, then there's an animation that sort of 234 00:16:26,676 --> 00:16:30,826 tries to exemplify this. These lines are lines of constant value 235 00:16:30,826 --> 00:16:33,679 of r. The, sort of, punitive distance from the 236 00:16:33,679 --> 00:16:37,051 black hole. And far away from the black hole, you see 237 00:16:37,051 --> 00:16:40,228 that the constant r surface might look like this. 238 00:16:40,228 --> 00:16:45,091 And so this coordinate could be thought of as distance from the black hole. 239 00:16:45,091 --> 00:16:49,889 But as you move closer in, lines of closer distance to the black hole look 240 00:16:49,889 --> 00:16:55,090 more and more like this. and then, the line, r equals, 241 00:16:55,090 --> 00:17:00,356 our Schwarzschild, is exactly the horizon, and after that we see something 242 00:17:00,356 --> 00:17:04,186 funky happening. The line, changing R now is no longer a 243 00:17:04,186 --> 00:17:07,742 motion in space, changing R becomes a motion in time. 244 00:17:07,742 --> 00:17:12,667 And indeed this region over here is something called the singularity. 245 00:17:12,667 --> 00:17:15,744 Once you are inside, and we'll talk about its. 246 00:17:15,744 --> 00:17:21,147 significance, once you are inside the black hole, anything you do even if you 247 00:17:21,147 --> 00:17:26,673 move at the speed of light in either direction, you are bound to land on this 248 00:17:26,673 --> 00:17:31,514 boundary here. That is your future, so the singularity of a black hole is not a 249 00:17:31,514 --> 00:17:36,418 place, it looks from infitinity like a place. The singularity at the center of a 250 00:17:36,418 --> 00:17:40,763 black hole is in fact a time. It's a when, not a where. It's everybody's 251 00:17:40,763 --> 00:17:43,612 future once you enter the black hole. So now, 252 00:17:43,612 --> 00:17:46,372 okay, penetrate through the horizon. 253 00:17:46,372 --> 00:17:51,184 Note that this is quite possible. You can be an observer here. 254 00:17:51,184 --> 00:17:56,008 And, there are definitely, inertial trajectories that take you 255 00:17:56,008 --> 00:17:59,577 through the horizon. What happens when you cross the horizon? 256 00:17:59,577 --> 00:18:04,275 Well, once you cross the horizon, here is what happens to you once you'er inside 257 00:18:04,275 --> 00:18:08,617 the horizon, you can make an easy calculation within a finite proper time. 258 00:18:08,617 --> 00:18:12,840 You reach the singularity, that crazy contour at the top of the diagram. 259 00:18:12,840 --> 00:18:16,941 What is a singularity? A singularity is a place where the tidal 260 00:18:16,941 --> 00:18:22,020 acceleration, remember this is the actual gravitational effects, go to infinity. 261 00:18:22,020 --> 00:18:26,955 And the verges literally becomes infinite that means that first your feet get 262 00:18:26,955 --> 00:18:32,016 ripped off from the rest of you but then eventually your atoms get ripped apart 263 00:18:32,016 --> 00:18:35,180 mattin matter gets decomposed by the title forces. 264 00:18:35,180 --> 00:18:37,614 And then what? As you get even closer to the 265 00:18:37,614 --> 00:18:40,326 singularity. Well, then things become infinite and 266 00:18:40,326 --> 00:18:44,531 this divergence, this infinity in the calculation, signals a breakdown of the 267 00:18:44,531 --> 00:18:47,298 equations. The truth is that I told you, at some 268 00:18:47,298 --> 00:18:50,507 point that Einstein's theory of relativity was incomplete. 269 00:18:50,507 --> 00:18:53,164 This infinity is a signal of its incompleteness. 270 00:18:53,164 --> 00:18:54,990 It cannot predict. We do not know. 271 00:18:54,990 --> 00:18:59,029 We do not have a theory that predict what happens when you fall onto the 272 00:18:59,029 --> 00:19:02,128 singularity or what happens to the material of the star. 273 00:19:02,128 --> 00:19:06,444 Remember the star in it's own, time, receded inside its Schwarzschild radius 274 00:19:06,444 --> 00:19:10,847 and then every bit of the star. In finite proper time as measured by 275 00:19:10,847 --> 00:19:15,960 Europe by its clock crashed into the singularity and then, 276 00:19:15,960 --> 00:19:20,906 because we don't have an equation that describes it, and hopefully some day we 277 00:19:20,906 --> 00:19:21,220 will.