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## Black holes

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**Black holes**Philip Freeman Roberta Tevlin**Curiouser and CuriouserWhat are black holes?**Can you get there from here? Do black holes really form? How? Seeing is believing (maybe) Observing Black Holes**first… (no, not a word from our sponsors)**What do we already know about Black Holes?**Everything I need to know about physicsI learned from**movies…. • 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. • <play video in player> • Try searching “Planet Vulcan owned by Black Hole”**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**Concept Test**Which path would the earth follow right after the sun was turned into a black hole? B A Before C D**What would happen:**The sun’s mass is the same, so there is no change in gravity. Therefore there is no change in the earth’s orbit! A**Many of our students have the idea that black holes have**special/extra forces that “suck in” everything. Help! The gravitational pull of something with 1/10th the mass of a hemoglobin molecule is destroying the planet! The fears some people had about the LHC are rooted in the same idea.**So… what is a black hole really?**• And what are they like?**The Big Idea: A history of the concept**• Classical Black Holes (dark stars) • Outlandish Results from Relativity • (Why are black holes so impossibly weird, and three impossible ways to think about them!)**Newton’s gravitation**• 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!**If mass is large enough, and r is small enough, then Light**can’t escape!**Light can’t escape if r is small enough**Notice how light particles slow down and fall back into the star? Does that seem a bit odd?**At first the idea that light was a wave seemed to make all**this irrelevant • Michell (1783), Laplace (1796): “Look! Particles of light can’t escape from a really big star!” • Young (1803) “But light’s a wave.” • Everybody: “Oh, never mind!” • Einstein (1916): “But light’s still affected by gravity!” • Everybody: Woah… weird!!**Einstein showed that gravitation causes (or more precisely**gravity IS) a ‘slowing down’ of time. If the field is strong enough (well, actually if the potential is ‘deep’ enough) then time stops! (and if that wasn’t 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 there’s so much downsizing!) Extra: Brief into to General Relativity**Inside a gravitational field time is slowed**Compared to this clock This clock is slower Equations**being deeper in a gravitational “well” slows down time!**• With a strong enough field time is STOPPED • Stronger still and… what??**Singularities?**• 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”**Falling into a black hole (don’t try this at home)**Help! The closer you get the slower time goes I’ve fallen And I c a n ’ t G e t Ouu… At least as seen from OUTSIDE**But this is not the whole picture**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:**Another viewpoint:**• 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!**An Analogy**And the observers suffered only briefly!**Going over Niagara falls with no barrel:**• 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:**From outside:**• 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.**A message horizon:**• 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: The message horizon… Last message to arrive (very late) Any further messages go down the falls with you… This fish swims in one place**What happens as you go over the fall is dependent on who is**observing it! • What do your friends upriver observe on the basis of your fish signals as you go over the falls? • 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 you observe yourself as you go over the falls? This could be a bit subtle, so let’s try a “think, pair, share” on this one! • Think about it for a minute • Then we’ll signal for you to pair up with another participant and see if you agree • Then we’ll discuss it together briefly.**What happens at the event horizon is dependent on who is**observing it! • 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-Painlevé metric, which describes black holes in exactly this way!**How is it that Your messages slow down and stop… but time**doesn’t stop for YOU as you fall in? 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! What’s 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**No escape:**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!**Frozen star vs black hole**Dynamic(but doomed) Static(and kinda boring)**At the centre: The singularity**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”**Three ways to think about the black hole’s event horizon**• Warped spacetime (time axis switches to “inward”) • Point of no return (escape velocity > c) • Infallingspacetime(homing fish) Extra: Why is this everybody’s picture of a black hole?**More ways to think about the unthinkable**We’ve already looked briefly at a black hole as an extreme of warped spacetime… but this is pretty tricky if we aren’t comfortable with general relativity (ok, it’s pretty tricky even if you are… )! Multiple models can help us to understand by giving different angles on the issues, so let’s briefly review two other models we looked at for event horizons. There are more!**Three ways to think about black hole event horizons**See More See More Models help us think, but they also SHAPE our thinking!**SO… What IS a Black Hole?**• 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 can’t be seen (cosmic censorship)**Anatomy of a very simple black hole:**Now that we understand the importance of the event horizon, let’s 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.**A cautionary note:**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 hole’s event horizon? Even this is fanciful… you couldn’t really even push it in. When lowered from the outside the ruler is ‘piling up in time’ near the horizon!**Anatomy of a very simple black hole:**Well Outside:Gravity is more-or-less normal. Photon sphere: Here light would orbit the black hole! Inside photon sphere:There are no stable orbits here. Fire your engines like the dickens to get out! Event horizon: no return past this point Inside: Your time axis is now pointed at the singularity. Singularity: where spacetime ends… Here be dragons! Schwarzschild Black Hole**Summary: Anatomy of a very simple black hole:**Event horizon: no return past this point Photon sphere: Here light would orbit the black hole! Inside: strong and erratic tidal effects (mixmaster physics) Singularity: where spacetime ends… Here be not yet understood quantum effects Here Be DRAGONS Schwarzschild Black Hole**How much more complex can a black hole get?**• 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!”.**Spinning and/or charged black holes**• If a black hole is spinning and/or has charge then the picture is a little (but only a little) more complex. Event horizon(s) (one outer, one inner) ` Ergosphere: There is no ‘standing still’ in this region, everything must rotate with the hole Besides… But we have to draw the line somewhere or this presentation will never end! Extra: More on effects near a black hole Singularity Extra: A VERY short mention of deeper results There are a LOT of dragons!**There is more we could look at, but for now it is time to go**on… Extra: Some black hole connections Continue to:Do black holes really form, and how?**Making a Black Hole**Black holes are very outlandish things! You well might ask yourself whether they could really exist.**are there REALLY such things as black holes?**• None of this would matter if black holes never actually formed… and for a long time that’s 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 isn’t a trivial point) We now know that black holes will indeed form, even under real ‘imperfect’ conditions.**Concept Test**Which of the following will create a black hole (you may indicate more than one) A star like the sun A star that starts off 4 times as massive as the sun A star that starts off 40 times as massive as the sun The large hadron collider**This is actually a very complicated question!**• 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: This isn’t a great table because what happens to stars depends a lot on what mix of elements goes into them in their formation, so all ranges are suspect! Extra: See some pretty graphs**Massive Stars**Inside a star there is a balance between gravitational pull and the outward pressure caused by heat.**At the end of its life the star (after considerable drama)**cools and pressure drops Drama Queen