Philip FreemanRoberta Tevlin

A relatively general

introduction toBLACK HOLES

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

What do we already know about Black Holes?

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.

<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

A B

C D

Which path would the earth follow right after the sun was turned into a black hole?

Before

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

1/10th 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!)

Compared to this clock

This clock is slower

Equations

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 fallen

And I c a n ’ t

G e t

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.

Tim

e ax

is 1

Tim

e ax

is 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?

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!

In which we remind ourselves

that we have described the event horizon in multiple ways, all of

them bizarre!

Model Strengths Weaknesses

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

THREE WAYS TO THINK ABOUT BLACK HOLE EVENT HORIZONS

MODELS HELP US THINK, BUT THEY ALSO SHAPE OUR THINKING!

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

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

Continue to:Do black holes

really form, and how?

Extra: Some black hole

connections

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 sunB.A star that starts off 4 times as massive as the sunC.A star that starts off 40 times as massive as the sunD.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 Mass Ends by Final Mass Becomes

<8 solar masses quietly settling down <1.4 solar masses White dwarf

8 – 20 solar masses Type II supernova 1.4 – 2.6? solar masses neutron star

20 – 50 solar masses Type II supernova 2.6 – 20 solar masses black hole

50ish – 100ish solar masses

Type I a/b supernova <2.6 solar masses neutron star / white dwarf

VERY big stars may not supernova >10 solar masses black 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.”