Catching waves with Kip Thorne
by The Plus Team
Kip Thorne has been at the forefront of black hole cosmology
since the early 1960s, and currently heads one of the world's
leading groups working in relativistic astrophysics. An important
emphasis of his research is on black holes and gravitational waves,
and developing the mathematics necessary to analyse these objects.
Professor Thorne gave a talk on "Warping Spacetime" and the
Plus team went along and spoke with him about it afterwards.
A little history
Have you ever wanted to witness the collision of two black holes?
You can, if you just listen hard enough for the symphony of
gravitational waves such events produce. Thorne is looking forward
to the coming decade, when the next generation of gravitational wave
detectors will reveal these hitherto unseen cosmic cataclysms.
To date, the study of black holes has advanced using theoretical
rather than experimental means, moving forward via the leaps of
intellectual insight contributed by the major players in the field.
The gravitational wave detectors being built by Thorne's colleagues
will provide the first opportunity to test theoretical predictions
made during the "Golden Age" of black hole theory, 1964 to 1974.
In this area of physics, the technology for actually testing
theoretical predictions has always lagged behind; for example, it
has only recently caught up enough to test some of the fundamental
consequences of Einstein's theory of general relativity with high
In 1915 Einstein introduced the world to the idea that gravity
was actually a warping effect of matter on spacetime , the 4
dimensional fabric that makes up our universe (there are 3
dimensions for space, and an extra dimension for time). The effects
and manifestations of this warping, as predicted by general
relativity, are much more complex than the familiar earthly effect
of apples falling from trees.
When Karl Schwarzschild solved the Einstein field equation (the
mathematical relationship between the curvature of spacetime and the
presence of matter) for a special type of star, he discovered an
object that was cut off from the rest of the universe - a black
Schwarzchild discovered that there is a critical size for a star,
which depends on the star's mass. If the star's volume shrinks down
to this critical size, the star's mass warps spacetime so extremely
that the curvature of spacetime measured at the star's surface is
singularity [Drawing used by permission of Kip
Surprisingly, the Schwarzchild singularity is not actually a
singularity in the terms defined by modern physics. Instead, it
describes the "horizon" of an entity known as a "black hole".
Anything that crosses the horizon and falls into the hole becomes
forever trapped, with no information able to escape from within the
hole's walls. In particular, no light can escape past the horizon,
hence the name "black hole".
Even though the notion of a black hole is a direct consequence of
general relativity, the world of physics (including Einstein
himself) refused to admit that such an outrageous object could
exist, and resisted the idea for over 50 years.
Resistance to the reality of black holes finally began to crumble
in the 1960s. It was then that the theoretical study of black holes
was accelerated into what Thorne calls the "Golden Age". During the
years between 1964 and 1974, many major discoveries were made by
Hawking, Penrose, Thorne and their contemporaries, and it is these
predictions that he wants to put to the test.
So what is a black hole?
A hole in the ground is not made of soil, but instead from the
empty space left after digging out the soil. In the same way, black
holes are made not from matter, but from a warping of spacetime
itself. To help us picture what a black hole looks like, Thorne uses
the analogy of a blind ant who lives on a large trampoline with a
heavy rock in the middle.
We human observers can see that the rock severely warps the
surface of the trampoline, which represents the ant's universe. The
tiny ant, on the other hand, will be unaware of this as it walks
along the surface of the large trampoline, effectively experiencing
it in only two dimensions.
The diameter is
greater than the circumference
[Drawing used by
permission of Kip Thorne]
The extreme curvature of the fabric of the ant's universe has
some surprising mathematical conseqences for geometry. Consider what
happens when the ant walks around the trampoline's "black hole",
measuring the circumference as it goes. In the normal (euclidean)
geometry of flat space, the diameter of a circle is its
circumference divided by pi. However, when the ant tries to measures
the diameter of the "black hole" by walking across it (all the way
down one side and up the other), it finds that the diameter is not
less than the circumference but in fact many times larger.
It is difficult for the ant to get a good understanding of its
universe by looking at the trampoline as a two-dimensional surface.
Similarly, if we consider a black hole in our own universe, we might
think of it as a sphere in our three-dimensional space. However,
because space is curved by the mass of the black hole, it turns out
that the only way we could see the entire curvature would be to
picture it in a flat space with many more dimensions than four!
Needless to say, most humans don't have a clue what
many-dimensional space might look like. To make the situation easier
to visualise, physicists instead just concentrate on two dimensions
of space (usually the "equatorial plane" that passes through the
middle of the black hole), and examine this plane's curvature in a
three-dimensional hyperspace. This gives us an extra mathematical
dimension to understand the curvature, but it is not a real
dimension that we can ever experience. It simply allows us to
examine the warping of a two-dimensional slice of our own spacetime,
just as we were able to examine the curvature of the blind ant's
[Drawing used by permission of Kip
In the physicists' model, there are three parameters that
describe the warping of spacetime - the curvature of space, the
warping of time and the whirl of space. These properties can be
described mathematically, and by solving the Einstein field equation
we can predict what these three parameters will be in various
circumstances. This helps us to picture black holes and other
relativistic phenomena. The picture at the right shows curvature,
warping and whirl for a spinning black hole which drags the
surrounding space with it as it spins.
Colliding black holes
A small black hole
orbiting a large black hole
[Drawing used by
permission of Kip Thorne]
As a small black hole orbits a larger black hole, it creates
gravitational waves which carry all the information required to
describe the warped spacetime around the two holes, the so-called
[Drawing used by permission of Kip
These waves are tidal waves, similar to ripples on the surface of
a pond. A cork on a pond's surface will be moved both back and forth
and up and down by the ripples. Similarly, gravitational waves also
produces motion in two directions by stretching and squeezing space.
Gravitational waves are very weak, however, stretching and squeezing
space by the width of just 1/10,000 of an atom when they reach the
Thorne is working with colleagues on a programme of gravity wave
detection using a technique known as laser interferometry. This
method involves splitting a laser beam into two perpendicular beams,
bouncing each of these two beams off a mirror, and then recombining
the two beams when they meet.
[Drawing used by permission of Kip
If the lengths of the two paths of the light differ, then the
recombined beams will form interference patterns from which the
differing lengths of the two paths can be deduced. As a gravity wave
passes through the L-shape of the interferometer, it will displace
the mirrors (attached to large masses) at the end of each arm,
altering the distances travelled by the beams and producing an
interference of the light.
LISA [Drawing used by permission of Kip Thorne]
LISA, the Laser Interferometer Space Antenna due to be launched
in 2011, is an interferometer on a massive scale. It will consist of
three separate space craft, arranged in space to form a triangle
with sides 5 million kms long. At this distance, it will take
approximately 20 seconds for light to travel between the space
craft. When passing gravitational waves stretch and squeeze space,
affecting the distance travelled by the light beams between the
space craft, this can be measured by the resulting interference of
the light beams.
Of course, making the measurements is a very subtle business.
Suppose LISA is trying to detect the waves produced by a system of
black holes 3 billion light years away, consisting of a small black
hole, weighing just ten times the mass of the sun, orbiting a large
black hole weighing one million times the mass of the sun. As the
gravitational waves will be very weak after travelling 3 billion
light years to our solar system, LISA will need to measure distance
variations of just 10-10 cms. LISA should be up to this
daunting task, and the waves it detects will carry detailed maps of
the big hole's space curvature, time warping and whirl.
[Drawing used by permission of Kip Thorne]
It is thought that colliding black holes will merge into a single
hole. Moreover, Hawking's Second law of black hole mechanics
predicts that after such collisions, the horizons must increase. In
other words, it is thought that the surface area of the final black
hole's horizon must be larger than the sum of the surface areas of
the two colliding holes' horizons.
The 4 kilometer
long, L-shaped, LIGO gravitational wave detector in Hanford,
[Photo used by permission of the LIGO
Project, California Institute of Technology]
The observational tests of this and other predictions will begin
this year with Earth-based gravity wave detectors (LIGO in Hanford,
Washington, along with a UK-German companion detector in Hanover and
a French-Italian companion detector in Pisa), and will be aided by
the eventual launch of LISA.
All of these predictions and observations are restricted to the
surface of the black hole. They can tell us nothing about the
singularity that lies hidden beneath the horizon. However, there is
one singularity we can study - the Big Bang which gave birth to our
Looking back to the
Big Bang [Drawing used by permission of Kip
From the Earth, astronomers have observed cosmic background
radiation enabling us to see back to just 100,000 years after the
Big Bang. Observation of neutrinos can take us back to when the
universe was only one second old. However, gravitational waves offer
the only direct tool to probe what the universe was like when it was
less than one second old.
Professor Thorne is very excited about the future for
gravitational wave detection. He looks forward to testing
theoretical predictions about black holes, and to a time when
gravitational waves show us the very birth of our galaxy itself.
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