Hello, welcome back, I m Dom and this is
the Map of Black Holes which isn t a map of where all the black holes are in space, it
s a concept map of the subject of black holes: laying out our current knowledge of them,
the evidence for their existence, and the many outstanding mysteries still to be solved;
they are very strange and fascinating indeed.
I find concept maps are really useful to give
you a good overall idea of a field of research, so here s the current state of
knowledge about black holes.
On Earth, getting into space in a space rocket
is really hard, because we need to climb out of the Earth s gravity well. But in a way
we re lucky. If the Earth was just fifty percent larger by diameter it would be impossible to get
into orbit with any of our current technology. This would mean no astronauts, no
satellites, no GPS or google Earth.
So the stronger the gravity of a planet, the
higher the escape velocity you need, and black holes are the most extreme example of this where
the escape velocity exceeds the speed of light. There is so much mass squeezed into such a small
volume that nothing can escape because nothing can travel faster than the speed of light Hence
the name: black hole, which weirdly comes from the black hole of calcutta, a notorious prison
where people went in but nobody ever left alive. Although this name, black hole, only caught
on in the late 1960s, before that they were referred to as dark stars, frozen stars
or gravitationally collapsed objects.
The original idea that black holes could
exist came from our understanding of Einstein's theory of relativity published in
1915, where gravity is explained as the curvature of spacetime. The more dense an object is the
more it curves spacetime, and the more curvature there is the stronger the force of gravity.
In 1916 Karl Schwarzchild found a solution to the field equations of relativity which
predicted a special distance from the black hole called the Schwarzchild radius,
but is also known as the event horizon, beyond which nothing can escape. This event
horizon was long considered a mathematical curiosity until the sixties and seventies
where theoretical developments and experimental evidence mounted up and people realised black
holes did actually exist in our universe.
This is a common visualisation of the
warping of spacetime around a black hole, although this is just a visual analogy. These
squiggly lines represent photons which are actually travelling in straight lines. They
only look like they curve around because they are travelling through a curved spacetime. This
phenomenon is known as gravitational lensing.
The inner horizon is a feature of a rotating
black hole. Rotating and non-rotating black holes have got distinct features which we ll
see when we look at their structures in a bit.
At the centre of the black hole is a singularity
where all of the mass of the black hole is squeezed into an infinitely small region of
infinite density creating an infinite curvature of spacetime. Well, that s probably not actually
true. This is a strong indication we are pushing the theory into a realm that it s not built to
cover. Really we need a theory of quantum gravity, and people think that if we could add the laws of
quantum mechanics to general relativity this could explain what is going on in the centre of a black
hole. A theory of quantum gravity is the holy grail of theoretical physics, which is why black
holes are so fascinating, because they are one of the few places in the universe where gravity
gets big enough to be as strong as the other three fundamental forces and so general relativity
and quantum mechanics are both needed to explain what is going on inside black holes.
Another way to visualise the motion of particles near a black hole is using space-time
diagrams. Far from a black hole, we see these squiggly lines travelling at 45 degrees which
represents light travelling at the speed of light. Because this is the cosmic speed limit, anything
with mass will have trajectories at some angle in between these limiting cases which is
traditionally referred to as a light cone. As you get closer and closer to the black hole
this light cone bends towards it due to the curvature of spacetime, and if you cross the event
horizon, all paths point inwards to the centre, which means whatever direction you travel
in you are always moving towards the centre of the black hole: every possible
future ends up with you getting squished. It s like space and time switch roles. Outside
the event horizon time only goes forwards, but inside the only direction you can move
is forwards in towards the singularity.
And it s called an event horizon because any event
that happens inside the black hole can never be seen by anyone outside. So it is literally the
horizon over which events can never be seen.
Most black holes that we know of are
created from the remnants of dying stars. When stars exhaust their fuel they perish in a
variety of dramatic ways depending on their mass.
Stars who s cores have a mass less than 1.4
times the mass of the sun collapse into white dwarf stars. Above this limit, known as the
Chandrasekhar limit, stars explode in a violent supernova and collapse into a neutron star. The
incredible pressure of all that matter in the core overcomes the electron s ability to repel each
other, known as electron degeneracy pressure, and the electrons and protons join together to make
an incredibly dense star made of pure neutrons.
Then above that the theory says that a
star with a mass in the core above 2.17 times the mass of the sun will collapse
into an even denser object: a black hole. There is a possibility there are other stars
more dense than a neutron star and less dense than black holes made of some form of exotic
matter, perhaps quark stars or strange stars, but these are hypothetical and we
have no evidence of them so far.
But exploding stars is only one mechanism for
black hole formation, there are giant black holes out there called supermassive black
holes with masses of millions of times to tens of billions of times the mass of the sun.
How they got so big is still an open question. Did they grow bigger over time by absorbing other
matter and black holes? Did they form from the universe s earliest massive stars? Or perhaps
they formed directly after the big bang from the primordial gas collapsing in on itself? We don
t yet know and this is still active research.
At the small mass scale it is theoretically
possible to have very low mass black holes. The key feature of a black hole is not so much
its mass, but the very high density of that mass, and so some people have wondered if tiny black
holes might be created in particle collisions like in the large hadron collider at CERN. You might
remember a media scare that there might be a black hole created in Switzerland that gobbled up the
Earth. But this was total nonsense because we get particles from space called cosmic rays with
way higher energies than anything we can create on Earth and anything that was created at CERN. And
they don t create black holes in the atmosphere, so there is absolutely no evidence that
miniature black holes are created from particle collisions so perhaps there is a lower
mass limit to black holes we don t know about, this is another open question.
Here is how the different masses of black holes are typically
classified according to mass and size:
Micro-black holes would have a mass up to the mass
of the moon, but would be tiny, having a radius of their event horizons of 0.1 millimetres or less.
Stellar black holes have approximately ten times the mass of the sun and are
about thirty kilometres in radius.
Intermediate black holes are about a
thousand times the mass of the sun, and are a similar size to the Earth with
a radius of about a thousand kilometres. Although the Earth actually has a radius of 6
thousand so I kind of got this picture wrong.
Supermassive black holes have masses from a
hundred thousand times the mass of the sun to tens of billions of solar masses and are so big they
get as big as four hundred astronomical units. For context, one astronomical unit is
the distance from the earth to the sun, so four hundred astronomical units is
about ten times the orbit of pluto. Which is insane to imagine a black hole that big.
Let s take a closer look at the anatomy of black holes. We ve already talked about the event
horizon and singularity, but there are many other interesting features we need to talk about.
Near a black hole clocks run slow. This is the effect of the highly curved spacetime which
causes time dilation. This means the experience of someone who is falling into a black hole
would be quite different to someone watching them fall in. If you travelled over the event
horizon, you wouldn t notice anything. But then, depending on the size of the black hole, it wouldn
t be long until you got completely spaghettified.
If, however, you watched someone falling into
a black hole, they would steadily move in slow motion as their local clock slowed down,
and get more and more red shifted until they looked like a red smudge on the event
horizon that gradually faded out of existence as the wavelength of light they
emit got longer and longer.
Then we have the singularity which I ve already
talked about, but basically it s a region of infinite curvature, where all the mass is squeezed
into zero volume with infinite density. But implies a breakdown of general relativity, and
really a theory of quantum gravity is needed.
Some more important features of a black
hole. Outside the black hole at 3 times the Schwarzchild radius is the innermost
stable circular orbit which is the minimum distance a test particle could orbit
the black hole in a circle and this marks the inner edge of an accretion disk
of infalling matter around a black hole.
And at 1.5 the Schwarzchild radius is the
photon sphere, which is the only possible circular orbit for a massless particle, and if
you sat here because photons are going all the way around the black hole you could look at the
back of your own head. It also marks the closest distance any elliptical orbit of any kind of
matter can get. If anything travels below this, it ll either get slingshotted out of the black
hole s gravity, or eventually spiral in.
Also black holes give off Hawking
radiation from the event horizon, although this is very very faint, and is
impossible for us to detect this unless we could somehow get very very close to a black hole.
It s worth noting here that black holes don t have any special suction powers where they
go around the galaxy hoovering everything up. The gravity of a black hole is the same shape
as any other massive body so, at a distance, being around a black hole would feel just like
being around any other star with the same mass, gravitationally speaking. They re special
because they are so dense, so when you get close in to them you experience a way higher
gravity than you could get anywhere else.
This picture only applies
to non-rotating black holes, the picture for a rotating black hole is
a little more complicated as shown here. Now you may wonder if you ever get non-rotating
black holes as everything in the universe is spinning in some way. But theoretically you can
get non-rotating black holes because Hawking radiation takes away some of the angular
momentum from the black hole, which would gradually slow down their spin, but it would
take a very very long time for this to happen.
Non-rotating black holes are spherical,
rotating black holes are a squashed oval shape. Also the singularity in the centre is
no longer a point, but a singularity ring. And they have a region outside the event
horizon called an ergosphere which is a region where it would be impossible to stand still
because the rotation of the black hole drags spacetime around it in a process called frame
dragging, kind of like a whirlpool of spacetime. And the frame dragging is so fast inside the
ergosphere you would have to travel faster than the speed of light just to stand still. So
you can move in the ergosphere, but only in the direction of the rotation of the black hole.
At the edge of the ergosphere is the innermost stable orbit, the minimum distance to the black
hole a particle can maintain a stable orbit.
Many real black holes are surrounded by an
accretion disk, a cloud of material that is falling into the black hole and generating loads
of heat and energy as the particles speed up and crash into each other. Accretion disks are
very bright sources of x-ray radiation and high energy particles which can fly out of the
ergosphere with way more energy than they entered, stealing angular momentum from the black
hole as they do so using it as a slingshot.
Finally, the incredible gravity around a
black hole leads to interesting gravitational lensing effects on the accretion disk
resulting in this familiar image. In reality the accretion disk
is actually a pancake shape, but we can see the accretion disk that would
be normally hidden behind the black hole, because the light from it which travels upwards
or downwards is bent around the black hole and comes towards us. So it looks like there is
an accretion disk above and below the black hole, but we are actually seeing the top and bottom of
the accretion disk that s behind the black hole.
I ve been talking for a long time, but
how do we know black holes actually exist? Well over the last 50 years we ve
built up a large body of observational evidence from many different techniques.
The first was from x-ray astronomy as the radiation from the accretion disk is mostly x-ray
radiation. The process that produces this x-ray radiation in the accretion disk is one of the
most efficient energy producing processes known where the spiralling material has up to 40% of its
rest mass converted into energy. To understand how hugely remarkable this is we can compare this
to the nuclear fusion process that powers the sun and all stars. Here only 0.7% of the rest
mass is converted to energy, way less than 40%. So the accretion disk is nearly sixty
times more violent than a burning star.
The very first black hole that was discovered
was discovered this way in 1971 and is called Cygnus X-1. Since then we have discovered
around a hundred more, although this is just a tiny sample of the number of black holes
that are thought to exist in our galaxy, and every single galaxy is thought to have
a supermassive black hole in its centre.
Often accretion disks are accompanied
by relativistic jets, which emit even higher energy particles and radiation than
from the accretion disk. The mechanism that creates these jests is not currently known.
We see many high energy sources in space, and we think many of them are caused by the accretion
of matter into black holes. These include active galactic nuclei, and quasars which are thought
to be the accretion disks of supermassive black holes, and also ultraluminous x-ray sources
thought to be from intermediate mass black holes.
Also things called x-ray binaries most
likely consist of a normal star and a black hole orbiting each other while the black
hole gradually sucks away matter from the star.
And short lived streamers are thought to be stars
which shine incredibly brightly as they are being swallowed up by a black hole before disappearing.
An entirely different line of evidence comes from the centre of our own galaxy by
tracking the orbits of about 100 stars which have been observed to be orbiting around an
invisible massive object called Sagittarius A*. By tracing the orbits and measuring the velocities
of the orbiting stars astrophysicists have been able to calculate the mass of the central body
to be a humongous 4.3 million times the mass of the sun, but this mass is confined to
a region of less than 0.002 light years, signs that it must be a supermassive black hole.
Even more recently in 2019 the first direct image of the accretion disk around a black
hole was constructed from the radio waves emitted by the galactic centre of the
Messier 87 galaxy, and it had the features of an accretion disk that we expected, if a
little blurry. But constructing this image was a feat of radio astronomy and was achieved by
combining the signals from 8 radio telescopes all around the world to create a virtual telescope
the size of the Earth; an amazing achievement.
Just as incredible was the detection
of gravitational waves by LIGO in 2016 which uses finely tuned lasers in a giant L shape
to detect the miniscule changes of distance caused by the rippling of spacetime when gravitational
waves passed through the Earth. The first gravitational waves they detected were created
by a pair of stellar mass black holes spiralling into each other and finally merging into a larger
black hole, and converting around 5% of their mass into gravitational waves. And since then LIGO
and VIRGO have detected many more collisions.
Finally there is a proposed method called
microlensing which has been seen many times for stars, but not as far as we know for black holes.
I ve talked about how the strong gravitational field around a black hole causes a lensing effect.
The idea is we could use this to detect black holes when they pass in front of a star. We ve
seen things like supernovae be gravitationally lensed by massive objects like entire galaxies.
But if we found a binary system where a star is orbiting a black hole we could potentially see
the radiation from the star being bent towards us as it passes behind the black hole which would
give us information about the black hole it is orbiting, and would be a really cool technique
for the future of black hole observations.
Let s take a quick look at the theoretical
understanding of black holes which started in 1916 but was really fleshed out in the 60s and 70s when
black holes were taken seriously as real physical objects, not just mathematical curiosities.
Here is the equation for the radius of a non-rotating black hole, which gives a
simple relationship with its mass where G is the gravitational constant and c is
the speed of light. But this gets more complicated if the black hole has spin or charge.
The general description of black holes, developed in the 60 s is called the no hair theorem and
states that a stationary black hole can be completely described by just three parameters:
mass, angular momentum and electric charge.
Then in the 70s a theory of black hole
thermodynamics was developed which describes the links between black hole mass and energy, how the
surface area of a black hole relates it s entropy, and how the surface gravity
relates to temperature.
Then Stephen Hawking applied quantum field
theory to black holes and showed that black holes radiate Hawking radiation energy from the
event horizon with a characteristic black body spectrum where the temperature is proportional
to the surface gravity of the black hole. So black holes will gradually lose their mass
over time by radiating away Hawking radiation, but this evaporation is slowest for the largest
black holes and fastest for the smallest black holes. Which means that micro-black holes would
be short-lived, but supermassive black holes will live for over 10^100 years which is a ludicrous
amount of time and those will be the last objects that will exist before the heat
death of the universe. What is going on? Oh it s just a car.
This all gives you a good idea about what we think we understand about black holes, but there
are many outstanding mysteries which we know about and these all seem to boil down to our
lack of a theory of quantum gravity.
I ve already mentioned how singularities
probably don t exist because they cannot be infinitely small with infinite density. So
there s a question: what actually happens to matter at the singularity? Unfortunately if we
ever found out experimentally, because of the event horizon we couldn t ever get the results
out to anyone which is a bit of an issue to ever figure out what s going on in the singularity.
Also, in the description of spinning or charged black holes there is a hypothetical possibility
of them containing an unstable wormhole which would let you leave the black hole but
in a completely different space time. They also have regions inside them where it
would be possible to travel to your own past along closed timelike curves which creates one
of those time-travel grandfather paradoxes. But, although these ideas are tantalizing
from a science fiction perspective, both of these will probably go away with a
proper quantum description of black holes.
There are other theoretical objects which have
been conjectured, but there is no evidence for them yet. These include stars somewhere in
between neutron stars and black holes but these are all highly speculative. Aslo white
holes which are like black holes but where the event horizon goes the other way. Information
can come out, but nothing can ever go in. And finally naked singularities which are
singularities which could be observed because they don t have an event horizon, but these are thought
to be unphysical and so not actually possible.
But these aren t as interesting
as the real theoretical puzzles. First of all is the holographic principle,
which is complicated to explain, but the general gist of it is that black holes might
be telling us the whole universe is a hologram. This is a strange result of the entropy of a black
hole. In every other thing in the universe entropy scales with the volume of that thing, but in
black holes it scales with the surface area, and this implies that anything that
happens within a volume of spacetime can be described by data on the surface of that
volume, so, we re all a hologram. But, again, we d need a theory of quantum gravity to
properly calculate the entropy of a black hole, so this is still active work.
Finally we have one of the biggest unsolved mysteries of black holes, what happens
to the information that falls into them? Now because black holes are defined by only three
parameters: mass, charge and angular momentum, any other information about objects that
fall into the black hole appears to be erased from the universe. But the thing is this isn t
allowed by a fundamental law of quantum mechanics called unitarity. So for example, an electron
has a load of quantum numbers associated with it that define it like lepton number, but
if an electron falls into a black hole this information is lost because the black hole only
preserves mass, charge, and angular momentum.
So one attempt to explain this is a
theory called complementarity which says the information does actually come
back out again, but in the Hawking radiation. The trouble was this was shown to
fail by a further paradox called the firewall paradox. Now the details of all these things
are complicated but the end result is that to resolve all these paradoxes about information we
may need to give up one of the fundamental rules in the laws of physics, either: Einstein s
equivalence principle, unitarity in quantum mechanics, or local quantum field theory.
But overall black holes are fascinating objects to study as they are the most extreme environments
in the universe where gravity and quantum physics meet and their very existence seems to break our
fundamental theories of physics. But by studying them the hope is we may actually uncover some
subtle clues that could help guide us to the next level of understanding so perhaps black
holes are actually the experimental key to developing a theory of quantum gravity, or perhaps
we ll just be a confused as we are now, forever.
