Alice through the looking glass

There have been a number of landmarks in the history of wormhole
physics. After the work of Einstein and Rosen in the mid-1930s
nothing much happened until John Wheeler, one of the greatest
physicists of the twentieth century (and the man who coined the
name black hole) published a paper in 1955. In it he showed for the first time that a tunnel in spacetime need not necessarily join
our Universe with a parallel one, but could bend round to join
two different regions of our Universe together (like the handle
on a coffee mug). It would be a tunnel that rose out of normal
spacetime providing an alternative route between its two ‘mouths’
through a higher dimension. Two years later he introduced the
word ‘wormhole’ into physics jargon in a landmark paper on what
he called ‘geometrodynamics’ which means the study of how the
geometry, or shape, of space changes and evolves. Of course his
work was still purely theoretical. Its aim was to understand what
shapes spacetime could be twisted into and had nothing to do with
the use of wormholes for humans to travel through. In fact, the
wormholes that Wheeler was interested in were extremely tiny
ones. He was studying the structure of spacetime on the minutest
possible scale where quantum mechanics tells us that everything
becomes fuzzy and uncertain. Down at this level, even spacetime
becomes frothy and foamy and all manner of strange shapes and
structures, including miniature wormholes, can form at random.
I will refer to these as quantum wormholes and we will meet them
again a little later on.
The next important event was in 1963 when New Zealand
mathematician Roy Kerr discovered that Einstein’s equations
predicted the existence of a completely new kind of black hole:
a spinning one, although he did not realize this at first. Only later
was it realized that Kerr’s solution applied to any spinning star
that collapsed to a black hole and that, since all stars are spinning
on their axes at various rates, Kerr’s black holes were more general
and more realistic than Schwarzschild’s non-spinning ones. What
is more, a black hole would spin much more rapidly than the
original star it formed from because it is so much more compact.
(Remember I drewthe analogy with the spinning ice skater when I
described such black holes in Chapter 4.) What was so interesting
about the results of Kerr’s calculations was the nature of the
singularity at the centre of such a black hole. It would no longer be
a zero-sized point like those at the centres of Schwarzschild black
holes but would be ring-shaped instead. The perimeter of the
ring is where all the matter is, and has almost zero thickness and hence nearly infinite density. The middle of the ring is just empty
space. Such a ring singularity could, depending on its mass and
spin, have a large enough diameter for humans and even their
spaceships to travel through1.
Oxford astrophysicist John Miller has pointed out that, while
Kerr’s solution uniquely represents the properties of spacetime
outside any stationary rotating black hole, there is as yet no
indication whatsoever that it correctly describes what goes on
inside the horizon, including everything about the ring singularity.
It is thus just one possible picture of what the inside of a black hole
might look like. Miller suggests that such descriptions should
come with a government health warning.
With this in mind, I will go ahead and describe what a Kerr
black hole might be like. To begin with, the ring singularity differs
in other ways fromSchwarzschild’s point singularity. For instance,
a ring singularity has a second, inner, horizon, called the Cauchy
horizon, which surrounds the singularity. Of course once you pass
through the outer event horizon there is no way back for you. But
you will at least be able to see light fromthe outside Universe, even
though it will be bent and focused by the gravity of the black hole.
The Cauchy horizon marks the boundary inside of which you will
no longer see light from the outside Universe. Now this might
sound reasonable enough at first sight, but don’t be fooled. Black
holes are such eerie places that nothing is straightforward. One of
the bizarre predictions of the mathematics of black holes is what
happens to the light you see from the outside Universe as you fall
closer towards the Cauchy horizon. Because your time is running
more and more slowly, time outside is speeding up until, at the
Cauchy horizon, time outside is running infinitely fast and you
would literally see the whole future of the Universe flash before
you at the instant you pass the horizon. I find this perversely apt;
just when you would expect to see your whole past flash before
your eyes, you see the entire future instead.
Just to make sure I don’t offend any black hole aficionados, I
should add that, in reality, you would not really have a privileged view of the future of the Universe since all the light that will ever
enter the black hole has to arrive all at once in a blink of an eye.
The light streaming in will be squashed towards the blue end of
the spectrum. This is the opposite of what is seen by an observer
outside a black hole watching light falling in. In that case, light is
stretched (redshifted). As you approach the Cauchy horizon you
see light being more and more blueshifted to higher and higher
frequency. This also implies that the light is gaining in energy
and you will be frizzled by that final burst of infinitely energetic
radiation. Sorry. Of course, all this is assuming you have survived
the gravitational tidal forces that will be stretching you and trying
to rip you apart before you get to the Cauchy horizon.
Let us for a moment put aside these trivial concerns of being
turned into spaghetti and then cooked in radiation and look a little
more closely at the singularity itself. The mathematics of general
relativity seems to suggest that a Kerr singularity is a window to
another universe. Instead of Alice falling down an Einstein–Rosen
bridge toWonderland, here is where she can step through the looking
glass. You see, provided you can make it as far as the singularity
itself, you might be able to travel through the centre of the ring
(making sure you do not get too close to the sides of course since
that is where the ‘stuff’ of the singularity is). Once you do this you
will have left our own spacetime behind for good.
So where would you travel to if you were to leap through this
cosmic ring of fire? The answer is that it depends crucially and
uncontrollably on the exact path you take through the singularity.
One possibility is that you would end up in a different part of
our own universe and, since time and space are mixed up, you
would almost certainly end up in a different time too. You might
emerge in the distant past or the distant future. [Great, you think,
here at last is a real time machine.] But aside from all the dangers
of jumping into the rotating black hole in the first place, going
through a Kerr singularity is a one-way trip. I do not mean that
you couldn’t go back through the ring fromthe other side once you
had jumped through, but simply that you would not find yourself
back where and when you started. Oh, and don’t forget there is
still the one-way event horizon that stops you from getting out. So let me summarize the pros and cons of a Kerr black hole
as a ‘star gate’. On the positive side, you can avoid being crushed
to zero size by carefully navigating through the centre of the
singularity. The problem with this is that, from outside the event
horizon, you cannot see what angle you should enter. Go in from
the side (along the plane of the ring) and you will not be able
to avoid spiralling in and hitting the ring. A more important
difference between the singularities inside rotating (Kerr) and
non-rotating (Schwarzschild) black holes is that space and time
are warped in different ways. In the jargon of relativity a point
singularity is called spacelike while a ring singularity is timelike.
Aspacelike singularity marks the edge of time (either its beginning,
like the Big Bang singularity, or its end as in a black hole) whereas
a timelike singularity marks the edge of space, which is how it can
serve as a window beyond our Universe.
All in all, it’s a shame about those two troublesome horizons
really. The event horizon allows one-way travel only, and it shields
the singularity from view so that we are not able to choose the
correct angle to enter. The Cauchy horizon, on the other hand, is
where you get zapped by infinitely blueshifted radiation. What
we would really like therefore is to get rid of these horizons,
leaving what is known as a naked singularity exposed to the
outside Universe. There are a number of ways of (maybe) getting
a naked singularity. One is through Hawking radiation, whereby
a black hole gradually evaporates until its horizon shrinks away
completely, leaving behind the exposed singularity. But this is
still highly controversial and many physicists believe that when
a black hole evaporates completely nothing is left behind. In any
case, this is only likely to happen to very tiny black holes and it is no
good waiting around for a rotating supermassive one to evaporate.
Such a black hole might, however, be stripped of its horizons in
a different way. You see, the faster a black hole is spinning the
further out its Cauchy horizon will extend and the closer it gets to
the outer event horizon. Spin it fast enough and the two horizons
overlap, and, at that instant, the mathematics predicts that they
cancel each other out and both will disappear.
A naked singularity might also form from the collapse of
a highly non-spherical mass, but this option is also speculative since such shapes are not likely to exist in the real Universe.
The prediction that this type of naked singularity might form
comes from complex computer simulations that astrophysicists
have studied.
I should remind you of course that most of what I have
said so far in this chapter is based on theoretical predictions and
speculations anyway. Physicists do not believe thatwewill ever be
able to go through a naked Kerr singularity and travel to another
universe or even to the other side of our own universe. Part of the
reason for their scepticism (and nervousness) is that if we could
we would also be able to use it as a time machine and, as we saw
in the last chapter, that is not an option many physicists are even
prepared to consider.
But there are a number of practical difficulties that look likely
tomakethe whole idea of travelling through such ring singularities
as impossible as trying to go through an Einstein–Rosen bridge. To
begin with, it doesn’t seem likely that any black hole could spin fast
enough to throw off its horizons. And very recent research seems
to indicate that the Cauchy horizon is so unstable that as soon
as you pass through it (even if you are on course to go through
the centre of the singularity) you will disturb it enough to turn it
into what is known as a null weak singularity, but a singularity
nevertheless, and you would be trapped inside.