- You can never see
anything enter a black hole. (bell dings) Imagine you trap your
nemesis in a rocket ship and blast him off towards a black hole. He looks back at you shaking
his fist at a constant rate. As he zooms in, gravity gets stronger, so you would expect him to speed up, but that is not what you see. Instead, the rocket ship
appears to be slowing down. Not only that, he also appears to be shaking his fist slower and slower. That's because from your perspective, his time is slowing down at the very instant when he
should cross the event horizon, the point beyond which
not even light can escape, he and his rocket ship do not disappear, instead, they seem to stop frozen in time. The light from the spaceship
gets dimmer and redder until it completely fades from view. This is how any object would look crossing the event horizon. Light is still coming from
the point where he crossed, it's just too redshifted to see, but if you could see that light, then in theory you would see everything that has ever fallen into the black hole frozen on its horizon, including
the star that formed it, but in practice, photons are
emitted at discreet intervals, so there will be a last photon
emitted outside the horizon, and therefore these images
will fade after some time. - This is just one of the strange results that comes outta the general
theory of relativity, our current best theory of gravity. The first solution of Einstein's equations predicted not only black holes, but also their opposite, white holes. It also implied the existence
of parallel universes and even possibly a way
to travel between them. This is a video about the
real science of black holes, white holes, and wormholes. - The general theory of relativity arose at least in part
due to a fundamental flaw in Newtonian gravity. In the 1600s Isaac Newton contemplated how an apple
falls to the ground, how the moon orbits the earth
and earth orbits the sun and he concluded that
every object with mass must attract every other, but Newton was troubled by his own theory. How could masses separated
by such vast distances apply a force on each other? He wrote, "That one body may
act upon another at a distance through a vacuum without the
mediation of anything else is to me, so great and
absurdity that I believe no man who has a competent faculty of thinking could ever fall into it." One man who definitely had a
competent faculty of thinking, was Albert Einstein and
over 200 years later, he figured out how gravity is mediated. Bodies do not exert forces
on each other directly. Instead, a mass like the
sun curves the spacetime in its immediate vicinity. This, then curves the spacetime around it and so on all the way to the earth. So the earth orbits the
sun, because the spacetime earth is passing through is curved. Masses are affected by the local curvature of spacetime, so no action
at a distance is required. Mathematically, this is described by Einstein's field equations. Can you write down the
Einstein field equation? - This was the the result of
Einstein's decade of hard work after special relativity and essentially what we've
got in the field equations on one side it says, tell me about the distribution
of matter and energy. The other side tells you
what the resultant curvature of spacetime is from that distribution of matter and energy
and it's a single line. It looks like, oh, this is
a simple equation, right? But it's not really one equation. It's a family of equations and
to make life more difficult, they're coupled equations, so
they depend upon each other and they are differential equations, so it means that there are integrals that have to be done, da, da da. So there's a whole bunch of
steps that you need to do to solve the field equations. To see what a solution to these
equations would look like, we need a tool to understand spacetime. So imagine your floating
around in empty space. A flash of light goes off above your head and spreads out in all directions. Now your entire future, anything that can and will ever happen to you
will occur within this bubble because the only way to get out of it would be to travel faster than light. In two dimensions, this bubble
is just a growing circle. If we allow time to run up the screen and take snapshots at regular intervals, then this light bubble traces out a cone, your future light cone. By convention, the axes are
scaled so that light rays always travel at 45 degrees. This cone reveals the
only region of spacetime that you can ever hope
to explore and influence. Now imagine that instead
of a flash of light above your head, those photons
were actually traveling in from all corners of the universe and they met at that instant and then continued traveling on in their separate directions. Well, in that case then into the past, these photons also reveal a light cone, your past light cone. Only events that happened inside this cone could have affected you
up to the present moment. We can simplify this diagram even further by plotting just one spatial
and one time dimension. This is the spacetime
diagram of empty space. If you want to measure how far apart two events are in spacetime,
you use something called the spacetime interval. The interval squared is
equal to minus dt squared, plus dx squared, since spacetime is flat, the geometry is the same everywhere and so this formula holds
throughout the entire diagram, which makes it really easy
to measure the separation between any two events, but around a mass, spacetime is curved and
therefore you need to modify the equation to take into
account the geometry. This is what solutions to
Einstein's equations are like. They tell you how spacetime curves and how to measure the
separation between two events in that curved geometry. Einstein published his equations in 1915 during the First World War, but he couldn't find an exact solution. Luckily, a copy of his paper made its way to the eastern front where
Germany was fighting Russia, stationed there was one of
the best astrophysicists of the time, Karl Schwarzschild. Despite being 41 years
old, he had volunteered to calculate artillery
trajectories for the German army. At least until a greater
challenge caught his attention, how to solve Einstein's field equations. Schwarzschild did the
standard physicist thing and imagined the simplest
possible scenario, an eternal static universe
with nothing in it except a single spherically
symmetric point mass. This mass was electrically
neutral and not rotating. Since this was the only
feature of his universe, he measured everything
using spherical coordinates relative to this center of this mass. So r is the radius and theta
and phi give the angles. For his time coordinate, he
chose time as being measured by someone far away from the mass, where spacetime is essentially flat. Using this approach,
Schwarzschild found the first non-trivial solution to
Einstein's equations, which nowadays we write like this. This Schwarzschild metric
describes how spacetime curves outside of the mass. It's pretty simple and
makes intuitive sense, far away from the mass
spacetime is nearly flat, but as you get closer and closer to it, spacetime becomes more and more curved, it attracts objects in
and time runs slower. (gunshots firing) Schwarzschild sent his
solution to Einstein, concluding with, "The war
treated me kindly enough in spite of the heavy gunfire to allow me to get away from it all and take this walk in
the land of your ideas." Einstein replied, "I have read your paper with the utmost interest,
I had not expected that one could formulate the
exact solution to the problem in such a simple way." But what seemed at first quite simple, soon became more complicated. Shortly after Schwarzschild
solution was published, people noticed two problem spots. At the center of the
mass, at r equals zero, this term is divided by zero,
so it blows up to infinity and therefore this equation breaks down and it can no longer describe
what's physically happening. This is what's called a singularity. Maybe that point could be excused, because it's in the middle of the mass, but there's another
problem spot outside of it at a special distance from the center known as the Schwarzschild
radius, this term blows up. So there is a second singularity.
What is going on here? Well, at the Schwarzschild radius, the spacetime curvature becomes so steep that the escape velocity, the
speed that anything would need to leave there is the speed of light and that would mean that inside
the Schwarzschild radius, nothing, not even light
would be able to escape. So you'd have this dark object that swallows up matter and light, a black hole, if you will, but most scientists doubted
that such an object could exist, because it would require a lot of mass to collapse down into a tiny space. How could that possibly ever happen? (thrilling music) Astronomers at the time were studying what happens at the end of a star's life. During its lifetime the inward
force of gravity is balanced by the outward radiation pressure created by the energy released
through nuclear fusion, but when the fuel runs out,
the radiation pressure drops. So gravity pulls all the star
material inwards, but how far? Most astronomers believed
some physical process would hold it up and in 1926, Ralph Fowler came up with
a possible mechanism. Pauli's exclusion principles states that, "Fermions like electrons
cannot occupy the same state, so as matter gets pushed
closer and closer together, the electrons each occupy
their own tiny volumes," but Heisenberg's uncertainty
principle says that, "You can't know the position
and momentum of a particle with absolute certainty,
so as the particles become more and more constrained in space, the uncertainty in their momentum, and hence their velocity must go up." So the more a star is compressed, the faster electrons will wiggle around and that creates an outward pressure. This electron degeneracy
pressure would prevent the star from collapsing completely. Instead, it would form a white dwarf with the density much
higher than a normal star and remarkably enough
astronomers had observed stars that fit this description. One of them was Sirius B. But the relief from this
discovery was short-lived. Four years later, 19-year-old
Subrahmanyan Chandrasekhar traveled by boat to England
to study with Fowler and Arthur Eddington, one of
the most revered scientists of the time. During his voyage, Chandrasekhar realized that electron degeneracy
pressure has its limits. Electrons can wiggle faster and faster, but only up to the speed of light. That means this effect
can only support stars up to a certain mass,
the Chandrasekhar limit. Beyond this, Chandrasekhar believed, not even electron de degeneracy pressure could prevent a star from collapsing, but Eddington was not impressed. He publicly blasted Chandrasekhar saying, "There should be a law of nature to prevent a star from
behaving in this absurd way" and indeed scientists did discover a way that stars heavier than
the Chandrasekhar limit could support themselves. When a star collapses
beyond a white dwarf, electrons and protons fuse together to form neutrinos and neutrons. These neutrons are also fermions, but with nearly 2000 times
the mass an electron, their degeneracy pressure
is even stronger. So this is what holds up neutron stars. There was this conviction among scientists that even if we didn't know the mechanism, something would prevent
a star from collapsing into a single point and
forming a black hole, because black holes were just
too preposterous to be real. The big blow to this belief
came in the late 1930s when Jay Robert Oppenheimer
and George Volkoff found that neutron stars
also have a maximum mass. Shortly after Oppenheimer
and Hartland Snyder showed that for the heaviest stars, there is nothing left to save
them when their fuel runs out, they wrote, "This contraction
will continue indefinitely," but Einstein still couldn't believe it. Oppenheimer was saying that
stars can collapse indefinitely, but when Einstein looked at the math, he found that time freezes on the horizon. So it seemed like
nothing could ever enter, which suggested that either there's something we don't understand or that black holes can't exist, (star explodes) but Oppenheimer offered a
solution to the problem. He said to an outside observer, you could never see anything go in, but if you were traveling
across the event horizon, you wouldn't notice anything unusual and you'd go right past it
without even knowing it. So how is this possible? We need a spacetime
diagram of a black hole. On the left is the
singularity at r equals zero. The dotted line at r equals
2M is the event horizon. Since the black hole doesn't move, these lines go straight up in time. Now let's see how ingoing
and outgoing light ray travel in this curved geometry. When you're really far away, the future light cones are
at the usual 45 degrees, but as you get closer to the horizon, the light cones get narrower and narrower, until right at the event horizon, they're so narrow that
they point straight up and inside the horizon, the
light cones tip to the left, but something strange happens
with ingoing light rays. - They fall in, but they
don't get to r equals 2M, they actually asymptote to that value as time goes to infinity, but they don't end at infinity, right? Mathematically they are
connected and come back in and they're traveling in this direction and this bothered a lot of people, this bothered people like Einstein, because he looked at
these equations and went, "well, if nothing can cross
this sort of boundary, then how could there be black holes? How could black holes even form?" - So what is going on here? Well, what's important to recognize is that this diagram is a projection. It's basically a 2D map of four dimensional curved spacetime. It's just like projecting
the 3D Earth onto a 2D map. When you do that, you
always get distortions. There is no perfectly accurate way to map the earth onto a 2D surface, but different maps can be
useful for different purposes. For example, if you wanna keep
angles and shapes the same, like if you're sailing across the ocean and you need to find your bearings, you can use the Mercator projection, that's the one Google Maps uses. A downside is that it misrepresent sizes. Africa and Greenland
look about the same size, but Africa is actually
around 14 times larger. The Gall-Peters projection
keeps relative sizes accurate, but as a result, angles
and shapes are distorted. In a similar way, we can
make different projections of 4D spacetime to study
different properties of it. Physical reality doesn't change, but the way the map describes it does. - He had chosen to put a
particular coordinate system of a space and have a time
coordinate, and off you go. It's the most sensible thing to do, right? - [Derek] People realize
that if you choose a different coordinate system by doing a coordinate
substitution, then the singularity at the event horizon disappears. - It goes away. That problem goes away and
things can actually cross into the black hole. - What this tells us is that there is no real physical singularity
at the event horizon. It just resulted from a poor
choice of coordinate system. Another way to visualize what's going on is by describing space as flowing
in towards the black hole, like a waterfall. As you get closer, space starts flowing in faster and faster. Photons emitted by the
spaceship have to swim against this flow, and this
becomes harder and harder the closer you get. Photons emitted just outside the horizon can barely make it out, but
it takes longer and longer. At the horizon, space falls in as fast as the photons are swimming. So if the horizon had a finite width, then photons would get stuck here, photons from everything that ever fell in, but the horizon is infinitely thin. So in reality, photons either
eventually escape or fall in. Inside the horizon, space falls faster than the speed of light, and so everything falls
into the singularity. So Oppenheimer was right. Someone outside a black hole
can never see anything enter because the last photons they can see will always be from just
outside the horizon, but if you yourself go, you will fall right
across the event horizon and into the singularity. Now you can extend the waterfall model to cover all three spatial dimensions, and that gives you this, a real simulation of space flowing into a static black hole made by my friend
Alessandro from ScienceClic. Later we'll use this model
to see what it's like falling into a rotating black hole. Now, I've never been
sucked into a black hole, but sometimes it feels like
it when I'm stuck on the phone with a spam collar. Fortunately, today's
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sponsoring this part of the video and now back to spacetime maps. If you take this map and transform it so that incoming and outgoing light ray all travel at 45 degrees
like we're used to, then something fascinating happens. The black hole singularity on the left transforms into a curved line at the top and since the future always
points up in this map, it tells us that the
singularity is not actually a place in space, instead,
it's a moment in time, the very last moment in time for anything that enters a black hole. The map we've just created
is a Kruskal-Szekers diagram, but this only represents
a portion of the universe, the part inside the
black holes event horizon and the part of the
universe closest to it, but what we can do is
contract the whole universe, the infinite past, infinite
distance, and infinite future, and morph it into a single map. It's like using the
universe's best fish eye lens. That gives us this penrose diagram. Again, light rays still
always go at 45 degrees. So the future always points up. The infinite past is in
the bottom of the diagram. The infinite future at the top and the sides on the right
are infinitely far away. The black hole singularity
is now a straight line at the top, a final moment in time. These lines are all at the same distance from the black hole. So the singularity is at r equals zero, the horizon is at r equals 2M, this line is at r equals 4M, and this is infinitely far away. All of these lines are at the same time. What's great about this map
is that it's very easy to see where you can still go and
what could have affected you. For example, when you're here,
you've got a lot of freedom. You can enter the black
hole or fly off to infinity, and you can see and receive
information from this area, but if you go beyond the horizon, your only possible future
is to meet the singularity. You can still, however,
see and receive information from the universe. You just can't send any back out. Now think about being at
this point in the map. This is at the event horizon, and now your entire future
is within the black hole, but what is the past of this moment? Well, you can draw the past light cone and it reveals this new region. If you're inside this region, you can send signals to the universe, but no matter where you
are in the universe, nothing can ever enter this region because it will never be
inside your light comb. So things can come out, but never go in. This is the opposite of a
black hole, a white hole. What color is a white hole? (Geraint exhales) (Derek laughs) - I mean, it's gonna be the, it's not gonna have a color, right? It's gonna be whatever's
being spat out of it. It depends what's in
there and gets thrown out, that's what you are going to see. So if it's got light in
there, it's got mass in there, it's all gonna be ejected. So the white hole kind of picture is the time reverse
picture of a black hole, instead of things falling in,
things get expelled outwards and so whilst a black hole has a membrane, the Schwarzschild horizon,
which once you cross, you can't get back out, the
white hole has the opposite. If you're inside the event
horizon, you have to be ejected, so it kicks you out kind of thing, right? Relativity doesn't tell
you which way time flows. There's nothing in there that
says that, that is the future and that is the past. When you are doing your mathematics and you're working out
the behavior of objects, you make a choice about which
direction is the future, but mathematically, you could have chosen the other way, right? You could have had time point
in the opposite direction. Any solution that you find in relativity, mathematically, you can just flip it and get a time reverse solution and that's also a
solution to the equations. - [Derek] Now, we've been showing things being ejected to the right,
but they could just as well be ejected to the left. So what's over there? This line is not at infinity, so there should be something beyond it. If we eject things in this direction, you find that they enter
a whole new universe, one parallel to our own. - [Geraint] We can fall
into this black hole, and somebody in this universe here could fall into this black
hole in their universe, and we would find ourselves
in the same black hole. (Derek chuckles) - The only downside is that we'd both soon end up in the singularity. I guess I'm just trying to understand where that universe appears in the mathematical part of the solution. Like, can you point to the part
of the equation and be like, so that's our universe,
and then these terms here, that's the other universe,
or do you know what I mean? Like-
- Yeah, well, it's coordinates, right? Imagine somebody, right, came
up with a coordinate system for the earth, but only
the northern hemisphere and you looked at that
coordinate system, right? And you looked at it and you said, "Ah, I can see the coordinate
system, it looks fine, but mathematically latitudes
can be negative, right? You've only got positive
latitudes in your solution. What about the negative ones?" And they said to you,
(scoffs) "Negative ones? No southern hemisphere, right?" And you've gotta go, "Well,
the mathematics says that you can have negative latitudes. Maybe we should go and
look over the equator to see if there is something down there" and I know that's a
kind of extreme example, because we know we live on a globe, but we don't know the full geometry of what's going on here in the sense that Schwarzschild laid down coordinates over part of the solution. It was like him only
laying down coordinates on the northern hemisphere and other people have come along and said, "Hey, there's a southern hemisphere" and more than that, there's two earths. That's why it's called maximal extension. It's like, if I have this
mathematical structure, then what is the extent of the coordinates that I can consider? And with the Schwarzschild black hole, you get a second universe that has its own independent
set of coordinates from our universe. I want to emphasize right,
this is the simplest solution to the Einstein field equations, and it already contains a black hole, white hole and two universes. - [Derek] That's what you get when you push this map to its limits so that every edge ends at
a singularity or infinity. - And in fact, there's another
little feature in here, which is that, that little
point there where they cross, that is an Einstein Rosen Bridge. - To see it, we need
to change coordinates. Now this line is at constant crustal time and it connects the
space of both universes. You can see what the spacetime is like by following this line from right to left. Far away from the event horizon, spacetime is basically flat, but as you get closer
to the event horizon, spacetime starts to curve more and more. At this cross, you are
at the event horizon, and if you go beyond it, you
end up in the parallel universe that gives you a wormhole
that looks like this. - So that is hypothetically
how we could use a black hole to travel from one universe to another. - Hypothetically, because these wormholes aren't actually stable in time. - It's a bit like a bridge,
but it's a bridge that is long and then becomes shorter
and then becomes long again and if you try to traverse this bridge, at some point, the bridge
is only very short, right? And you say, "Oh, well, let
me just cross this bridge." But as you start crossing
the bridge and start running, your speed is finite, right? The speed of light roughly
and then the bridge starts, becoming stretching and you
never come out the other side. - [Derek] This pinching
off always happens too fast for anything to travel through. You can also see this if you
look at the Penrose diagram, because when you're inside one universe, there isn't a light cone that can take you to the other universe. The only way to do that would be to travel faster than light, but there might be another way. Schwarzschild solution
describes a black hole that doesn't rotate. Yet, every star does rotate and since angular momentum
must be conserved, every black hole must also be rotating. While Schwarzschild found
his solution within weeks after Einstein published his equations, solving them for a spinning mass turned out to be much harder. Physicists tried, but 10 years
after Schwarzschild solution, they still hadn't solved it. 10 years turned into
20, which turned into 40 and then in 1963, Roy
Kerr found the solution to Einstein's equations
for a spinning black hole, which is far more complicated
than Schwarzschild solution and this comes with a
few dramatic changes. The first is that the structure
is completely different. The black hole now
consists of several layers. It's also not spherically
symmetric anymore. This happens because the rotation causes it to bulge around the equator. So it's only symmetric
about its axis of spin. Alessandro from science
click simulated what happens around this spinning black hole. Space gets dragged around
with the black hole taking you and the
particles along with it. When you get closer,
space gets dragged around faster and faster until
it goes around faster than the speed of light, you've now entered into
the first new region, the ergosphere. No matter how hard you
fire your rockets here, it's impossible to stay still
relative to distance stars, but because space doesn't
flow directly inward, you can still escape the black hole. When you travel in further,
you go through the next layer, the outer horizon, the point of no return. Here you can only go inwards, but as you get dragged
in deeper and deeper, something crazy happens,
you enter another region, one where you can move
around freely again, so you're not doomed to the singularity. You're now inside the inner event horizon. Here you can actually see the singularity - In a normal black hole, it's a point, but it in a rotating black hole, it actually expands out to be a ring and there are weird things happened with spacetime inside the
center of a black hole, a rotating black hole, but it's thought that you can actually fly through the singularity. - [Derek] We need a Penrose diagram of a spinning black hole,
where before the singularity was a horizontal line at the top here, the singularity lifts
up and moves to the sides, revealing this new region
inside the inner horizon. Here we can move around freely
and avoid the singularity, but these edges aren't at
infinity or a singularity, so there must be something beyond them. Well, when you venture further, you could find yourself in a white hole, which would push you out
into a whole nother universe. - You can have these pictures whereby you're in one universe, you
fall into a rotating black hole, you fly through the singularity, and you pop out into a new
universe from a white hole, and then you can just
continue playing this game. - Extending this diagram infinitely far. but there is still one
thing we haven't done, brave the singularity. So you aim straight towards
the center of the ring and head off towards it,
but rather than time ending, you now find yourself in
universe, a strange universe, one where gravity pushes instead of pulls. This is known as an anti-verse. If that's too weird,
you can always jump back across the singularity
and return to a universe with normal gravity. - And I know this is basically
science fiction, right? But if you take the
solutions of relativity at, you know, essentially at face
value and add on a little bit, which is what Penrose
does here, he says this, "oh look, these shapes are very similar, I can just stick these together." Then this is the conclusion that you get. Now we have effectively an infinite number of universes all connected
with black hole, white holes all the way through and
you, of you go to explore, but it'll be a very brave
person who's the first one who's gonna leap into
a rotating black hole to find out if this is correct? (Derek chuckles) - Yeah, I would not sign up for that. So could these maximally
extended Schwarzschild and Kerr solutions
actually exist in nature? Well, there are some issues. Both the extended Schwarzschild
and Kerr solutions are solutions of eternal black
holes in an empty universe. - As you say, it's an eternal solution. So it stretches infinitely
far into the past and infinitely far into the future and so there's no formation
mechanism in there, it's just a static solution and I think that is part of the, part of the reason why black holes are realized in our universe
and white holes aren't- - Or might not be. - Or might not be, or I'm reasonably I, personally, I'm reasonably confident that they don't exist, right? - [Derek] For the maximally
extended Kerr solution, there's also another problem. If you're an immortal
astronaut inside the universe, you can send light into the black hole, but because there's
infinite time compressed in this top corner, you can
pile up light along this edge, which creates an infinite flux of energy along the inner horizon. This concentration of energy then creates its own singularity, sealing off the ring
singularity and beyond. - My suspicion and the suspicion of some other people in the field is that this inner horizon will become singular and you will not be able to go
through these second copies. - So all the white holes,
wormholes, other universes and anti universes disappear. Does that mean that real
wormholes are impossible? In 1987, Michael Morris and
Kip Thorne looked at wormholes that an advanced civilization could use for interstellar travel,
ones that have no horizons, so you can travel back and
forth, are stable in time, and have some other properties like being able to construct them. They found several
geometries that are allowed by Einstein's general relativity. In theory, these could
connect different parts of the universe, making a
sort of interstellar highway. They might even be able to
connect to different universes. The only problem is that
all these geometries require an exotic kind of matter with a negative energy density to prevent the wormhole from collapsing. - This exotic kind of matter, is really against the
loss of physics, so it's, I have the prejudice
that it will not exist. I'm bothered by the fact that we say that the science fiction wormholes
are mathematically possible. It's true, it's mathematically possible in the sense that there's
some geometry that can exist, but Einstein's theory
is not just geometries, it's geometries plus field equations. If you use the kinds
of properties of matter that matter actually has,
then they're not possible. So I feel that the reason
they're not possible is very strong. - So according to our
current best understanding, it seems likely that white
holes, traversable wormholes, and these parallel universes don't exist, but we also used to think
that black holes didn't exist. So maybe we'll be surprised again. - I mean, we have one universe, right? Good, why can't we have two. (whimsical music)
