So black holes exist and they are an 
important part of the constitution of 
galaxies and they are the end point of 
stellar evolution for mass of stars and 
most of them we don't see. 
But if they happen to have a bindery 
partner we can detect the accretion discs 
around them. 
Okay, what can we say about these objects 
from understanding GR. 
What do 
people's studies tell us. the black holes 
we've been considering have been the 
simplest, spherically symmetric, 
non-rotating, simple objects. 
how complicated can black holes get? 
Well, they can get complicated, but it 
turns out not very. 
there's a beautiful theory known 
colloquially as the Black Hole No Hair 
theorem, or a black hole has no hair. 
it turns out that in the collapse from a 
star to a black hole, all of the 
properties of the stars are lost. 
The chemical composition makes no 
difference. 
The temperature is gone, 
the shape of something that collapsed is 
gone. 
All of those features are radiated away 
as gravitational waves or energy. 
All that information is gone in the 
collapse. 
Black holes are completely characterized 
by three numbers. 
Tell me three properties of a black hole, 
and I can exactly describe, 
that is all there is to say about it. 
We said that stars are by and large 
described by mass, but the stars also 
have magnetic fields, and rate of 
rotation, and [INAUDIBLE], chemical 
composition, and metallicity, and age. 
No such thing for a black hole. 
A black hole is completely characterized 
by its mass, 
its angular momentum and its electric 
charge. 
Now, electric charge is expected to be 
zero. 
Why would a black hole carry an electric 
charge? 
Everything in the universe is pretty much 
neutral. 
we know that its mass. 
We can measure if something's orbiting 
it. 
Angular momentum is expected to be rather 
large. 
Remember, this is a collapsed neutron 
stars. 
These neutron stars we saw are in a 
collapsed core. 
When it collapsed to a neutron star, it 
carried enough angular momentum to drive 
a pulsar. 
We expect most black holes to be rotating 
rapidly. 
the Schwarzchild example that was the 
topic of the simulations we've been doing 
was a simplified case with vanishing 
angular momentum. 
Angular momentum makes it a lot more 
complicated to understand, 
but that's all there is. 
There's only that one extra parameter. 
The second thing is, we discussed this 
very special, spherical symmetric case, 
and we found the singularity. 
Maybe that's a artifact of the symmetry 
of the situation. 
This was a real consideration when the 
black hole solutions were first 
discovered. 
work of Hawking and Penrose shows that 
no, this is real. 
general relativity is a theory which when 
you start with an initially smooth and 
reasonable un, non singular space time 
you can prove that within a finite time 
in the future, or possibly in a finite 
time in the past, you had actual 
singularities. 
General relatively produces singularities 
starting from non-singular initial 
conditions, and then it doesn't know what 
to do, 
which means that relativity as a theory 
is intrinsically incomplete. 
We know that we don't have the final word 
on gravity, and some of us are trying to 
do better, but at the moment this is what 
we have. 
Do we need to care about what happens at 
the singularity? 
Well, again we will never see what 
happens at the singularity, at the center 
of the black hole, because we don't see 
anything inside the horizon. 
There's this light like-surface 
surrounding it, and light cannot escape, 
so in some sense maybe we don't care. 
there is a conjecture called the cosmic 
censorship conjecture, 
which is our model of base, which says 
that all singularities are hidden inside 
horizons, 
which means, things that are not 
described by the equations might be going 
on in your theory. 
But they're going on in places, that have 
no causal effect on anything that's 
happening outside. 
We could go there and investigate them, 
though we'd never come back to tell, 
but they will never influence anything 
about us. 
The inside of a black hole has no impact 
on the exterior of a black hole. 
Nothing can escape, 
not even light. 
so this is the cosmic censorship 
hypothesis. 
there are indications that it may fail 
and that there maybe such things 
violating it, as singularities not hidden 
behind horizons. 
Those would be naked similarities, and 
there is recent evidence that such things 
are in fact possible in reasonable 
gravitational theories, but we of course 
have not observed any. 
in the realm of fantasy, let's look again 
at this image of the black hole that I 
showed you, where you remember that I 
described this is the outside of the 
black hole. This as the inside of the 
black hole. 
This was the singularity, and this was 
the horizon. 
This was the line r equals r 
Schwarzschild, which was lake like, in 
fact, and yeah well this is the black 
hole, this is the outside. 
What is the rest of this? 
and, this region, and I should note, 
this, description, is a description that 
is valid for a region just outside the 
horizon. 
That's why I was using it. 
But it's obtained by ignoring completely 
the fact that there's a star. 
you're basically using the solution to 
the part of Einstein's equations where 
you set the energy and momentum bit to 
zero. 
Which is true, everywhere outside the 
star. 
So those are the equations you solve to 
describe everything except where 
materials are. 
Most of space is free of matter and 
energy. 
It's mostly vacuum. 
And so we use those equations and then 
you, you get that solution, you can 
extend that solution. 
So in real life there would be a big fat 
star over here and while you could hit 
the singularity, just like most of the 
matter in the star is, all of this stuff 
down here and to the left would be 
complete fantasy. 
But let's imagine, we've drawn a valid 
solution to Einstein's equations anyway. 
we don't know how to create such a thing, 
but what does this look like. 
Well so there's this region out here 
which is the outside. 
There's this region out in here which is 
the black hole. 
There's this region in here which is 
interesting. 
Notice that you can't get into that 
region no matter what you do. 
Remember time moves this way. 
you would have to be moving faster than 
light. 
To tip through this light cone. 
This is what's called a white hole. 
Everything can only come out of it, 
nothing can ever fall into it. 
It's a time reversed version of a black 
hole. 
And this region out here, it turns out, 
looks a lot like this region out here. 
So there is another asymptotic region. 
And away from the black hole, it looks 
quite reasonable. 
Like normal space time. 
And so, remembering that time runs 
vertically. 
You now have this great description of 
two regions, which, 
outside, the outsides, that look like the 
outside of a black hole, 
which are disjoint, right? 
They, they don't touch each other. 
Except at this, one point. 
they actually intersect, and this one 
point is just, too short. 
The, the, length of time that these two 
universes are connected, if you want, is 
just too short for a light beam to get 
from here to here. 
A light beam sort of that can travel the 
boundary from one to the other. but, this 
is the idea for what is called a 
wormhole. 
A small deformation of this leads to 
something called the Einstein-Rosen 
Bridge, where there is a sort of finite 
time where the space time on the right, 
space time on the left are connected. 
that is the origin of the idea of worm 
holes. 
You can imagine that somewhere in our 
space time is a horizon, and there is a 
sort of a, a length of time during which 
by going through that region of strong 
curvature. 
You could come out and go completely 
different universe or into a part of our 
own universe that is very far you could 
imagine sort of our universe bending over 
and a wormhole cutting through or some 
such nonsense. 
And at the moment 
we don't have any, working solutions. 
So the Einstein-Rosen Bridge has been 
shown to be unstable, 
Any perturbation anywhere, would, 
collapse it down, 
People have been working on various ways 
to modify the solutions to get wormholes 
that are both stable. 
And last long enough for, at least a, a 
photon or a particle to get through and 
maybe something macroscopic. 
that has not happened, but there is no 
theorem that I know of, that precludes 
its existence, 
and so maybe there are solutions to the 
equations that generate wormholes, and 
maybe, 
maybe, there are actually wormholes out 
there. I cannot exclude that, 
and then what's on the other side could 
be a different universe, could be a 
different part of our own universe. 
Going through a wormhole would be an 
exciting thing to think about. 
I didn't want to leave you without them. 
And then the last thing I wanted to 
discuss is quantum issues of black holes. 
And so it's a result again due to Hawking 
that quantum effects, the quantum 
fluctuations near a horizon 
violate this idea that a black hole 
produces no energy and in fact a black 
hole does emit radiation. 
It's called Hawking radiation. 
It's not a property of general relativity 
which is a classical theory. 
It's a property of the quantum fields, 
electromagnetic fields and electron 
fields and whatever other fields you have 
in your theory fluctuating near, in the 
presence of the large curvatures at black 
holes horizon. 
And 
That means that a black hole radiates, 
and Hawking's calculation of the black 
hole radiation led him to, later figure 
out that a black hole radiates black body 
radiation. 
A black hole has a temperature. 
The thermodynamics of a black hole was 
later developed. 
It's, quite a developed art, but it's a 
weird object. 
The temperature of a black body, 
decreases with its mass, of a black hole, 
decreases with its mass. 
It's inversely proportional to its mass. 
Bigger black holes are cold. 
Smaller black holes, less massive black 
holes, are hot. 
So, smaller black holes, that means, 
radiate more. 
This is very strange because when a black 
hole radiates of course a the energy came 
from the black holes mass so the black 
hole become loses mass, becomes a little 
bit smaller and therefore a little bit 
hotter. 
A black hole is one of those weird 
objects with negative specific heat. 
As it loses heat, it heats up. 
Typically, objects lose energy and they 
cool. A black hole heats as it loses 
energy. 
So as it loses energy it heats more, it 
loses, it radiates more. 
Remember T to the fourth, it heats more, 
it radiates more. 
So the end of a black holes life would be 
a very dramatic explosion. 
In fact the title of Hawking's paper was 
Cosmic Explosions, because he was 
thinking about, maybe we should go look 
for these black holes that at the end of 
their life produce these very explosive, 
high temperature, large amounts of 
radiation and black holes can completely 
disappear, evaporate. 
That's not a big worry it turns out. 
the expected lifetime of a five solar 
mass black hole is on the order of the 
ten to the 62 years, given a universe 
that is ten to the ten or so years old. 
That's not yet a major concern. 
But if there are tiny black holes around, 
that therefore radiate more. 
We know about million solar mass black 
holes. 
Those last even longer. 
We know about stellar mass black holes. 
Those last too long, 
but if some mechanism produced two kilo 
black holes or 
proton mass black holes, those would 
evaporate much more rapidly. 
And the possibility of microscopic black 
holes, and their evaporation is something 
that people are studying in various, both 
theoretical, and at the LHC, even 
experimental level, to try to see if they 
can form a black hole and watch it 
evaporate essentially as part of their 
high energy collisions. 
So, this is the theory bit of the black 
hole.