Transcript Slide 1

BLACK HOLES
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

FIRST… (NO, NOT A WORD FROM OUR SPONSORS)
What do we already know about Black Holes?
UNIVERSITY OF HOLLYWOOD:

In which we realise that
sometimes movies and TV are
not to be trusted!

EVERYTHING I NEED TO KNOW ABOUT PHYSICS
I 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?
A
B
C
D
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.
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

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!)
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)
The closer you
get the slower
time goes
Help!
I’ve fallen
And I c a n ’ t
Ge 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

Note: No actual fish were
harmed in the production of
this example!
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)
This fish swims
in one place
Any further
messages go
down the falls
with you…
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?

What do you observe yourself as you go over the falls?
This
could
be a bit subtle,
let’s
try a “think,
pair,
share”
The
fish-signals
from so
the
observer
going
over
the
onfalls
this one!
arrive with lower and lower frequency, until
• Think about it for a minute
they stop altogether. But this does not mean that
• the
Thenobserver
we’ll signal
you to at
pairthe
up message
with another
is for
stopped
horizon,
participant
andlast
see if
you agreeis.
only
that the
message
•
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 GullstrandPainlevé 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?
Time axis 1
As you fall into a black hole your time as seen by
you and your time as seen by an outside (nonfalling)
observer seem
to be really different!
Well, remember
from Special
What’s
with
that?
Relativity
that
differences in
time were due to two
observers’ time axes pointing in
different directions.
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
Static
Dynamic
(and kinda boring)
(but doomed)
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)
Extra: Why is
• Infalling spacetime (homing fish)
this everybody’s
picture of a
black hole?
MORE WAYS TO THINK ABOUT THE UNTHINKABLE

In which we remind ourselves
that we have described the event
horizon in multiple ways, all of
them bizarre!

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
Model
Strengths
Weaknesses
Warped Spacetime
Good to understand
the extreme nature of
event horizon and
singularity
Allows us to calculate
the size of event
horizon, very close to
classical
Good to understand
what happens if you fall
into horizon
Hard to understand
what happens as you
fall past horizon
Tipped lightcone,
extreme curvature
Point of No Return
No escape from horizon
Infalling spacetime
Waterfall analogy
TOO close to classical,
risks being confused
with the “dark star”
idea.
Can lead to some
misconceptions,
doesn’t convey the
horizon from outside.
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:
Photon
sphere
Well
Outside
: :
Inside
photon
Here light
would
Gravity
is more-or-less
sphere
:
orbit
the black
hole!
normal.
There are no stable
Inside
: YourFire
time
Event
horizon
:
orbits here.
axis
isengines
now
pointed
no
return
past
this
your
like
at
the
singularity.
point
the
dickens
to get
out!
Singularity:
where spacetime
ends…
Here be dragons!
SCHWARZSCHILD BLACK HOLE
SUMMARY: ANATOMY OF A VERY SIMPLE BLACK HOLE:
Event horizon:
Photon sphere:
no return past this
point
Here light would
orbit the black hole!
Inside: strong and
erratic tidal effects
(mixmaster physics)
SCHWARZSCHILD BLACK HOLE
Singularity:
where spacetime
ends…
Here be not yet
Here
Be
understood
DRAGONS
quantum effects
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)
Besides…
Ergosphere: There
is no ‘standing
in have to draw the line
Butstill’we
Extra: More on
effects near a
this region,
black hole
`
everything
must
somewhere
or this presentation
will
rotate with the hole
Singularity
never end!
There are a LOT of dragons!
Extra: A VERY
short mention
of deeper
results
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

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.
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.
B.
C.
D.
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:
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
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
THE END RESULT DEPENDS ON THE MASS OF
THE STAR.
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.
OTHER THINGS THAT COULD (PERHAPS) CREATE
BLACK HOLES.


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?
CAN NEW PHYSICS SAVE THE WORLD FROM
BLACK HOLES?


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
BUT THE CONDITIONS FOR BLACK HOLES OCCUR IN
REALMS WHERE CLASSICAL PHYSICS ONLY NEED APPLY…



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!
LOCATING BLACK HOLES



Be vewy vewy quiet,
We’re hunting Black Holes!

So, if black holes DO exist... How do we
find them?
Let’s start with what they look like.
WHITEBOARD EXERCISE
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.
THE SKY AT NOON (POST BLACK HOLE)
Regular night sky (except for season)
WHY DON’T WE SEE ANYTHING?

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!)
FROM A DISTANCE

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 DO WE SPOT THEM FROM FAR AWAY?
1) BLACK HOLES ARE MESSY EATERS!

So, how can we identify a black hole if they
are different only up close?

We look for
stuff falling in!
INFALLING MATERIAL HEATED BY FRICTION AND
ACCELERATED BY TWISTED MAGNETIC FIELDS
Jet
Accretion Disk
2) LOOK FOR SOMETHING VERY VERY SMALL
AND MASSIVE!

Binary systems like Cygnus X-1 are
strong candidates.
GALAXIES: MAY ALL HAVE SUPERMASSIVE BLACK
HOLES AT THEIR CENTRES!
year
This is real data
showing the
positions of stars
in the centre of
our galaxy over
16 years of
observation
A LOT OF MASS IN NOT MUCH SPACE



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
SO WE KNOW WHERE TO LOOK FOR A REALLY BIG
BLACK HOLE VERY CLOSE BY!

We should be able to directly image Sgr A* within 10 years
WHERE CAN YOU USE / INTRODUCE THESE
IDEAS IN YOUR TEACHING?
“It’s black and it looks like a hole. I’d say it’s a black hole.”
END
(NOTE THAT ONLY A FRACTION OF THE SLIDES
WILL HAVE BEEN PRESENTED… DO CHECK OUT
THE RESOURCE WHEN IT IS POSTED!)