# 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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Philip Freeman Roberta Tevlin

 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

UNIVERSITY OF HOLLYWOOD:  In which we realise that sometimes movies and TV are not to be trusted! 

 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”

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

A B C D Which path would the earth follow right after the sun was turned into a black hole? Before

Draw the earth and sun on your whiteboards: Nice and big but leave room because we’ll be drawing some orbits!

Draw the present orbit of the earth around the Sun (with a dotted line)

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!

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!

 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.

 Some common responses What are some other possible answers? What do you think the reasoning is for each of these?

 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. 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!

 And what are they like?

 In which we see how a perfectly logical idea can, when carried to its logical conclusion, make everybody’s 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!)

 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!

Notice how light particles slow down and fall back into the star? Does that seem a bit odd?

 Michell (1783), Laplace (1796): “Look! Particles of light can’t escape from a really big star!”  Einstein (1916): “But light’s still affected by gravity!”  Everybody: Woah… weird!!  Young (1803) “But light’s a wave.”  Everybody: “Oh, never mind!”

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 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!)

 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)

 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!

 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!)

 If light is affected by gravity it should lose energy going up in a field, and gain energy when falling.  But it can’t slow down… so how does it lose energy?

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!

Compared to this clock This clock is slower Equations

If the “mass” of a ‘bit’ of light is based on its energy then:

 With a strong enough field time is STOPPED  Stronger still and… what??

 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”

Help!I’ve fallenAnd I c a n ’ t G e t Ouu…Ouu… The closer you get the slower time goes At least as seen from OUTSIDE

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:

 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!

 Note: No actual fish were harmed in the production of this example !  And the observers suffered only briefly!

 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:

 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.

 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…

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.  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?

 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!

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

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!

Static (and kinda boring) Dynamic (but doomed)

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”

Warped spacetime ( time axis switches to “inward”) Point of no return (escape velocity > c) Infalling spacetime (homing fish) Extra: Why is this everybody’s picture of a black hole?

 Recall that General Relativity shows that spacetime is “curved”...

 Curvature of the Earth’s 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:

 Take a flat slice through the star IN ANY DIRECTION. More area inside Than outside suggests More area inside Than outside suggests

1.It’s a 2D shape, but black holes are 3D surfaces. Black holes are black in all directions!

2.It creates a “double view” of gravity: Gravity is the curvature Gravity is “downward” Sorta?   

 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

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!

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 we’ll move on!

FlatSteep Flat

WITH SUFFICIENT MASS IN A SMALL ENOUGH SPACE THE CURVATURE BECOMES EXTREME: Point of no return

from xkcd (www.xkcd.com)

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!  I n which we remind ourselves that we have described the event horizon in multiple ways, all of them bizarre! 

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, doesn’t 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 !

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

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!

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 don’t have to worry about “where the space comes from” because space isn’t conserved – it isn’t a “thing”.

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.

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 isn’t 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 can’t escape.

 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)

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.

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!

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

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

 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!”.

 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

 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.

 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!

 Recall that an early test of General Relativity was the bending of starlight by the sun, changing The apparent position of stars:

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

As you fall through the horizon.

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.

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!

 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”

But eventually as you pass the event horizon the effects will become severe! Worse the effects are violent and unstable… one moment you’ll 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!”

Continue to: Do black holes really form, and how? Extra: Some black hole connections

 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

 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 doesn’t it?)

 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!

 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”

 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)

 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!

 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.

 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)

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

 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 <8 solar massesquietly settling down<1.4 solar massesWhite dwarf 8 – 20 solar massesType II supernova1.4 – 2.6? solar massesneutron star 20 – 50 solar massesType II supernova2.6 – 20 solar massesblack hole 50ish – 100ish solar masses Type I a/b supernova<2.6 solar masses neutron star / white dwarf VERY big starsmay not supernova>10 solar massesblack hole 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

Inside a star there is a balance between gravitational pull and the outward pressure caused by heat.

Drama Queen

Cygnus X-1, a black hole of about 15 solar masses with a visible companion

 Smaller masses don’t form a black hole.  Really big stars supernova and loose enough mass that they aren’t so big anymore (though still probably enough to make black holes).  These are called “stellar mass” black holes, and there are some likely suspects out there.

 In the early universe (high densities allow random clumps to make mini-black holes).  High energy collisions could create teeny tiny black holes, briefly. (Note: If our current ideas are correct the LHC has only 0.0000000000001% of the energy needed for this)  As yet unknown processes?

 We know that we DON’T know how gravity works when quantum effects start to matter.  Could these effects (or other new physics) mean there are no black holes after all? Quantum Gravity

 For large black holes there is nothing extreme about the conditions they would have to form under.  We know that there are things with masses large enough that they would have to become black holes eventually.  It seems there is no escaping the dragons!

 So, if black holes DO exist... How do we find them?  Let’s start with what they look like.  Be vewy vewy quiet, We’re hunting Black Holes! 

What would you see, looking up at noon, if the sun really did implode into a black hole? Describe or sketch on your white board.

Regular night sky (except for season)

 Black holes are black  The sun would be a small black hole  Effects from intensity are significant only very close to event horizon (around 3km!)

 We already know that from the outside the black hole is no different than any other mass.  But because it is so much more compact things can get a lot more intense  And that makes for some more intense effects  But only up close.

 So, how can we identify a black hole if they are different only up close?  We look for stuff falling in!

Accretion Disk Jet

 Binary systems like Cygnus X-1 are strong candidates.

year This is real data showing the positions of stars in the centre of our galaxy over 16 years of observation

 Fitted curves for this stellar motion near our galactic centre (SGR A*)  More than 4 million solar masses  In a space definitely smaller than the distance from the earth to the sun

 We should be able to directly image Sgr A* within 10 years

“It’s black and it looks like a hole. I’d say it’s a black hole.”

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