Philip Freeman Roberta Tevlin. A relatively general introduction to BLACK HOLES Curiouser and Curiouser What are black holes? Can you get there from.
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Post on 16-Dec-2015
Slide 1 Philip Freeman Roberta Tevlin Slide 2 A relatively general introduction to BLACK HOLES Curiouser and Curiouser What are black holes? Can you get there from here? Do black holes really form? How? Seeing is believing (maybe) Observing Black Holes Slide 3 What do we already know about Black Holes? Slide 4 UNIVERSITY OF HOLLYWOOD: In which we realise that sometimes movies and TV are not to be trusted! Slide 5 There is a video that goes here, but I have taken it from the slide show for fear of crashing things. You can find the youtube clip. Try searching Planet Vulcan owned by Black Hole Slide 6 WHAT WOULD HAPPEN IF THE SUN BECAME A BLACK HOLE? The sun could not become a black hole due to any known process, but suppose some special effect turns the sun into a black hole RIGHT NOW. What would happen? Looking at that answer can help us understand our existing understanding of black holes. Concept Test Whiteboard Exercise Slide 7 A B C D Which path would the earth follow right after the sun was turned into a black hole? Before Slide 8 Draw the earth and sun on your whiteboards: Nice and big but leave room because well be drawing some orbits! Slide 9 Draw the present orbit of the earth around the Sun (with a dotted line) Slide 10 What path do you think your students might predict after the Sun imploded? Draw the path(s) with a dashed line. Be ready to explain the reasoning! Slide 11 How would the orbit change if the sun were to suddenly implode into a black hole? Draw the new orbit with a solid line. Be ready to explain your reasoning! Slide 12 Current orbit: It is common to draw an ellipse, but at this scale the orbit is as close to circular as one can see or draw. Slide 13 Some common responses What are some other possible answers? What do you think the reasoning is for each of these? Slide 14 What would happen: The suns mass is the same, so there is no change in gravity. Therefore there is no change in the earths orbit! A Slide 15 Many of our students have the idea that black holes have special/extra forces that suck in everything. The fears some people had about the LHC are rooted in the same idea. Help! The gravitational pull of something with 1/10 th the mass of a hemoglobin molecule is destroying the planet! Slide 16 And what are they like? Slide 17 In which we see how a perfectly logical idea can, when carried to its logical conclusion, make everybodys head hurt! a)Classical Black Holes (dark stars) b)Outlandish Results from Relativity (Why are black holes so impossibly weird, and three impossible ways to think about them!) Slide 18 If light is made out of corpuscles (little bits) Then gravity should affect light And since light has a finite speed If a star is big enough light will not be able to escape! A DARK STAR! Slide 19 IF MASS IS LARGE ENOUGH, AND R IS SMALL ENOUGH, THEN LIGHT CANT ESCAPE! Slide 20 Notice how light particles slow down and fall back into the star? Does that seem a bit odd? Slide 21 Michell (1783), Laplace (1796): Look! Particles of light cant escape from a really big star! Einstein (1916): But lights still affected by gravity! Everybody: Woah weird!! Young (1803) But lights a wave. Everybody: Oh, never mind! Slide 22 Extra: Brief into to General Relativity If the field is strong enough (well, actually if the potential is deep enough) then time stops! (and if that wasnt bad enough, past that point gravity is so strong that nothing can stop things from collapsing to a mathematical point which seems a bit small, even in times when theres so much downsizing!) Slide 23 In which we see how a little relativity goes a long ways! Postulates of Relativity: All motion is relative (no experiment can detect absolute motion) The speed of light is the same always (no matter what the source or observer) Slide 24 New! Improved! Now with extra Geometry! Postulates of Relativity: All motion is relative (no experiment can detect absolute motion) The speed of light is the same always (no matter what the source or observer) A free falling frame IS an inertial frame! Slide 25 GR reunites gravity and light No gravity:Free falling: eg: equivalence principle says being inside a free falling frame is equivalent to a frame with no gravity So gravity must bend the path of a beam of light (from inside the elevator we have to see the light go straight, so from outside we see the path of light is bent!) Slide 26 If light is affected by gravity it should lose energy going up in a field, and gain energy when falling. But it cant slow down so how does it lose energy? Slide 27 Slide 28 A million billion waves = 2.5s No, a million billion waves = 1.2s Dude, your clock is slow! You mean your clock is fast! Counting the number of oscillations of a wave is how we DEFINE a second The light frequency must match all other clocks. TIME ITSELF IS SLOWED DOWN BY GRAVITY! Slide 29 Compared to this clock This clock is slower Equations Slide 30 If the mass of a bit of light is based on its energy then: Slide 31 Slide 32 With a strong enough field time is STOPPED Stronger still and what?? Slide 33 The GR equations blow up for strong fields! At a certain radius (the Event Horizon) time as seen from the outside STOPS. This radius is the most fundamental description of the black hole. Deep inside everything goes to infinity, and nothing makes any sense! Black Holes are Where God Divided by Zero Slide 34 Help!Ive fallenAnd I c a n t G e t OuuOuu The closer you get the slower time goes At least as seen from OUTSIDE Slide 35 The way in which objects seem to freeze (and fade out) as we watch from outside lead to an early misunderstanding about black holes, and an earlier name for them: the Frozen Star. Collasing star slows and freezes at the event horizon: Slide 36 One of the things than changed this view was the discovery of a description that followed the infalling star, rather than standing back and watching from outside. From this point of view things look very different, and the freezing does not mean things stop! Slide 37 Note: No actual fish were harmed in the production of this example ! And the observers suffered only briefly! Slide 38 Imagine you are going over a waterfall. You send messages out by attaching them to fish (like homing pigeons just go with it!)and sending them upstream to your friends: Slide 39 You will send out the fish at a regular frequency (Tweets? Blubs?): From outside the fish arrive one after the other, but as the water flows faster they are slowed down going upstream so they start to be spaced further apart. Slide 40 Eventually the water is flowing as fast as the fish can swim, so it no longer gets anywhere, it just swims as fast as it can in one place: Last message to arrive (very late) This fish swims in one place Any further messages go down the falls with you The message horizon Slide 41 This could be a bit subtle, so lets try a think, pair, share on this one! Think about it for a minute Then well signal for you to pair up with another participant and see if you agree Then well discuss it together briefly. The fish-signals from the observer going over the falls arrive with lower and lower frequency, until they stop altogether. But this does not mean that the observer is stopped at the message horizon, only that the last message is. What do your friends upriver observe on the basis of your fish signals as you go over the falls? What do you observe yourself as you go over the falls? Slide 42 Just like the fish-signals you sent as you went over a waterfall, the frequency of light signals is decreased as you fall in. The difference here is that the fishes swim more slowly, but light always travels at the same speed it loses energy instead (the gravitational red-shift). Also those light signals are tied to the nature of time, while the fish-signals are not. (People who fish may feel differently about that last) But the analogy is pretty good despite that. There is a full mathematical treatment, called the Gullstrand- Painlev metric, which describes black holes in exactly this way! Slide 43 As you fall into a black hole your time as seen by you and your time as seen by an outside (non- falling) observer seem to be really different! Whats with that? Well, remember from Special Relativity that differences in time were due to two observers time axes pointing in different directions. Time axis 1 Time axis 2 Slide 44 As you cross the event horizon your time axis is tipped so much that it now points AT THE CENTRE OF THE BLACK HOLE You can no more point your ship away from the singularity than you can drive your car away from tomorrow! Slide 45 Static (and kinda boring) Dynamic (but doomed) Slide 46 The event horizon is a critical and extreme place, but inside is stranger yet. At the centre of the black hole is the point where time is directed and where time ends. A single mathematical point which sooner or later (whatever that means in this context) contains everything that has ever fallen across the horizon. This is the SINGULARITY Black Holes are Where God Divided by Zero Slide 47 Warped spacetime ( time axis switches to inward) Point of no return (escape velocity > c) Infalling spacetime (homing fish) Extra: Why is this everybodys picture of a black hole? Slide 48 Recall that General Relativity shows that spacetime is curved... Slide 49 Curvature of the Earths surface: a circle on the earth has more area inside than the outside suggests: Curvature near a black hole: a sphere around a black hole has more volume inside than area suggests: Slide 50 Take a flat slice through the star IN ANY DIRECTION. More area inside Than outside suggests More area inside Than outside suggests Slide 51 1.Its a 2D shape, but black holes are 3D surfaces. Black holes are black in all directions! Slide 52 2.It creates a double view of gravity: Gravity is the curvature Gravity is downward Sorta? Slide 53 Remember that the direction they show things bulging in is NOT REAL it is not a 4 th dimension etc it is just a visual way to show that there is more inside than the perimeter would suggest. Extra Extra: time and curvature Back to main Slide 54 Remember that in the Alice and Bob general relativity activity we saw that the two models of gravity made different predictions about time. If Alice had stayed in one place she would have experienced LESS time than Bob! Slide 55 But this is backwards to the way it really works. The deeper into the gravity well the LESS time should pass. At this point I would show the Alice and Bob video Can we travel in time. You have already seen this though, so well move on! Slide 56 FlatSteep Flat Slide 57 WITH SUFFICIENT MASS IN A SMALL ENOUGH SPACE THE CURVATURE BECOMES EXTREME: Point of no return Slide 58 from xkcd (www.xkcd.com) Slide 59 Weve already looked briefly at a black hole as an extreme of warped spacetime but this is pretty tricky if we arent comfortable with general relativity (ok, its pretty tricky even if you are )! Multiple models can help us to understand by giving different angles on the issues, so lets briefly review two other models we looked at for event horizons. There are more! I n which we remind ourselves that we have described the event horizon in multiple ways, all of them bizarre! Slide 60 ModelStrengthsWeaknesses Warped Spacetime Tipped lightcone, extreme curvature Good to understand the extreme nature of event horizon and singularity Hard to understand what happens as you fall past horizon Point of No Return No escape from horizon Allows us to calculate the size of event horizon, very close to classical TOO close to classical, risks being confused with the dark star idea. Infalling spacetime Waterfall analogy Good to understand what happens if you fall into horizon Can lead to some misconceptions, doesnt convey the horizon from outside. See More See More T HREE WAYS TO THINK ABOUT BLACK HOLE EVENT HORIZONS M ODELS HELP US THINK, BUT THEY ALSO SHAPE OUR THINKING ! Slide 61 Slide 62 How big would the sun actually be if we turned it into a black hole somehow? A.A little smaller than Jupiter B.About the size of the earth C.About the size of Waterloo D.About the size of a basketball Slide 63 Slide 64 Answer: r s =3.0 km Slide 65 One mathematical model for a black hole, which corresponds roughly to the point of view of someone falling in, views spacetime itself as moving toward the black hole, rather like our waterfall analogy! Slide 66 In cosmology you considered space as expanding, so the idea of space moving is a concept which you have already considered. The red shift of light from distant stars can be understood as a stretching caused by this expansion, or equivalently, as a result of light moving against the expansion.. Note that you dont have to worry about where the space comes from because space isnt conserved it isnt a thing. Slide 67 The cosmological red shift can be thought of as the effect on the light of crossing the expanding space of the universe: At each point the light is going upstream against moving space (relative to you), though less and less as it gets closer. This motion upstream is one way to understand the red shift. Slide 68 In a similar way we can model gravitation as an inward fall of spacetime. Going against gravity is like trying to swim up a waterfall, and the gravitational red shift is akin to the cosmological redshift. Fall is in quotes here because this isnt a fall caused by gravity... Looked at in this way the inward velocity of the metric IS gravity! At the event horizon the velocity of the infall reaches the speed of light which is why light cant escape. Slide 69 Form when enough mass-energy is within a small enough radius (Schwarzschild radius) Contain singularities (places where spacetime stops existing -- whatever that means!) Are surrounded by event horizons, so that these singularies cant be seen (cosmic censorship) Slide 70 Now that we understand the importance of the event horizon, lets look at a very simple black hole and its anatomy. A black hole with no charge or spin is called a Schwarzschild black hole. It is totally describable by its Schwarzschild radius. Slide 71 We call the Schwarzschild radius the radius of the black hole all the time, but this is clearly not right. What would happen if you tried to measure the radius of a black holes event horizon? Even this is fanciful you couldnt really even push it in. When lowered from the outside the ruler is piling up in time near the horizon! Slide 72 Well Outside : Gravity is more-or-less normal. Inside photon sphere : There are no stable orbits here. Fire your engines like the dickens to get out! Singularity: where spacetime ends Here be dragons! Photon sphere : Here light would orbit the black hole! Inside : Your time axis is now pointed at the singularity. Event horizon : no return past this point Slide 73 Singularity: where spacetime ends Here be not yet understood quantum effects Inside : strong and erratic tidal effects (mixmaster physics) Photon sphere : Here light would orbit the black hole! Here Be DRAGONS Slide 74 Answer: not a lot. Black holes have no detailed structure, only mass, charge, and spin. All other details are radiated away, leaving a uniform event horizon with no detail, summed up by the statement that: BLACK HOLES HAVE NO HAIR!. Slide 75 If a black hole is spinning and/or has charge then the picture is a little (but only a little) more complex. Singularity ` Event horizon(s) (one outer, one inner) Ergosphere : There is no standing still in this region, everything must rotate with the hole But we have to draw the line somewhere or this presentation will never end! Besides There are a LOT of dragons! Extra: A VERY short mention of deeper results Extra: More on effects near a black hole Slide 76 There are many other effects that you might see/experience near the black hole. First: note that what you see depends in part on whether you are holding yourself outside the hole or if you are falling inward. This gives two very different ways to model and describe black holes. Slide 77 What the event horizon of a black hole looks like depends on your frame! Falling in (Inertial) Holding still (Accelerating) No clear boundary for event horizon No emitted particles (just virtual ones) Horizon is a conductive membrane with atmosphere of emitted particles! Slide 78 Recall that an early test of General Relativity was the bending of starlight by the sun, changing The apparent position of stars: Slide 79 Light from this star And appears to come from here Other stars are affected the same way So the entire sky is compressed into a circular cone. Is bent by gravity Slide 80 Slide 81 As you fall through the horizon. Slide 82 X If you are near a large mass your head is farther from the mass than your feet are. In many cases that difference is great enough to matter. Very close to a black hole it matters A LOT. Slide 83 X Lets calculate the classical force of gravity on your head and your feet to compare them: Mass of sun: m =2 10 30 kg G=6.7 10 -11 Nm 2 /kg 2 r s =3.0 10 3 m NOTE: This is too small for a black hole to form by usual means, but a larger black hole could eventually reduce to this size. Assume that: * your head and feet(plus boots) are each about 5kg * Your head is about 1.7m further from the black hole than your feet. Calculate: ( ignoring significant digits! ) F g,head = ? (force on your head) F g,fee t = ? (force on your feet) F g = ? (what is the difference?) Slide 84 X Answer: F g,head = 7.4358 10 13 N (force on your head) F g,feet = 7.4444 10 13 N (force on your feet) F g 9 10 10 N The force on your feet is quite a lot greater than the force on your head! Slide 85 F g 9 10 10 N Similar differences on your right and left sides lead to a compression sideways. X The effect would be like having your head tied to a support and 9,000 metric tonnes tied to your feet! !! The effects together are called spaghettification Slide 86 But eventually as you pass the event horizon the effects will become severe! Worse the effects are violent and unstable one moment youll be compressed sideways and stretched vertically, the next the opposite! This is called Mixmaster Physics Short Version: If someone invites you to take a trip into a black hole Say NO! Slide 87 Continue to: Do black holes really form, and how? Extra: Some black hole connections Slide 88 Over the past 50 years deep results have been discovered about black holes Links to thermodynamics (area entropy, surface gravity temperature, Hawking radiation black body radiation) Hints of the connection between gravity and QM Hints that the nature of the universe may be of LOWER dimension than we think Slide 89 Hawking shows The surface area of the event horizons of all the black holes in a region cannot decrease. AREA INCREASE THEOREM! (sounds a bit like entropy doesnt it?) Slide 90 Slide 91 YES! Entropy proportional to Area of Event Horizon Temperature proportional to gravitational acceleration at event horizon The smaller the black hole the higher its temperature! Slide 92 Black holes radiate black body radiation, in accordance to their temperature Hawking Radiation Virtual Particle pairs : background quantum foam Event Horizon : Hawking Radiation : some particle pairs are separated by the horizon one becomes real and the other falls in Slide 93 Temperature of a black hole is VERY low: for a T 6 10 7 K / M (M in solar masses) Mass will drop, but very very slowly Lifetime M 3 10 66 years (M in solar masses) Slide 94 Decrease in Area (entropy) made up for by entropy of random emitted radiation. Is there something more going on? What happens when the black hole vanishes? Information paradoxes? Other issues? Residue? Not-quite-random radiation? Jury is still out! Slide 95 In which we see that there is probably no escape from black holes in more ways than one! Black holes are very outlandish things! You well might ask yourself whether they could really exist. Slide 96 None of this would matter if black holes never actually formed and for a long time thats what people thought Maybe the equations describe that, but in reality something will keep it from happening. (this is what physicists currently think about white holes and some other concepts, so it isnt a trivial point) Slide 97 Which of the following will create a black hole (you may indicate more than one) A.A star like the sun B.A star that starts off 4 times as massive as the sun C.A star that starts off 40 times as massive as the sun D.The large hadron collider Slide 98 The fate of a star depends on the mass left when it reaches its final end and cools down enough for collapse Our best understanding of this is that: Starting MassEnds byFinal MassBecomes
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