|
BLACK HOLES
by
Ted Bunn
Einstein's General Relativity
Field Equations
What is a black hole?
 Loosely speaking, a black hole is a region of space that has so much
mass concentrated in it that there is no way for a nearby object to
escape its gravitational pull. Since our best theory of gravity at
the moment is Einstein's general theory of relativity, we have to
delve into some results of this theory to understand black holes in
detail, but let's start of slow, by thinking about gravity under
fairly simple circumstances.
Suppose that you are standing on the surface of a planet. You throw a
rock straight up into the air. Assuming you don't throw it too hard,
it will rise for a while, but eventually the acceleration due to the
planet's gravity will make it start to fall down again. If you threw
the rock hard enough, though, you could make it escape the planet's
gravity entirely. It would keep on rising forever. The speed with
which you need to throw the rock in order that it just barely escapes
the planet's gravity is called the "escape velocity." As you would
expect, the escape velocity depends on the mass of the planet: if the
planet is extremely massive, then its gravity is very strong, and the
escape velocity is high. A lighter planet would have a smaller escape
velocity. The escape velocity also depends on how far you are from
the planet's center: the closer you are, the higher the escape
velocity. The Earth's escape velocity is 11.2 kilometers per second
(about 25,000 m.p.h.), while the Moon's is only 2.4 kilometers per
second (about 5300 m.p.h.).
Now imagine an object with such an enormous concentration of mass in
such a small radius that its escape velocity was greater than the
velocity of light. Then, since nothing can go faster than light,
nothing can escape the object's gravitational field. Even a beam of
light would be pulled back by gravity and would be unable to escape.
The idea of a mass concentration so dense that even light would be
trapped goes all the way back to Laplace in the 18th century. Almost
immediately after Einstein developed general relativity, Karl
Schwarzschild discovered a mathematical solution to the equations of
the theory that described such an object. It was only much later,
with the work of such people as Oppenheimer, Volkoff, and Snyder in
the 1930's, that people thought seriously about the possibility that
such objects might actually exist in the Universe. (Yes, this is the
same Oppenheimer who ran the Manhattan Project.) These researchers
showed that when a sufficiently massive star runs out of fuel, it is
unable to support itself against its own gravitational pull, and it
should collapse into a black hole.
In general relativity, gravity is a manifestation of the curvature of
spacetime. Massive objects distort space and time, so that the usual
rules of geometry don't apply anymore. Near a black hole, this
distortion of space is extremely severe and causes black holes to have
some very strange properties. In particular, a black hole has
something called an 'event horizon.' This is a spherical surface that
marks the boundary of the black hole. You can pass in through the
horizon, but you can't get back out. In fact, once you've crossed the
horizon, you're doomed to move inexorably closer and closer to the
'singularity' at the center of the black hole.
You can think of the horizon as the place where the escape velocity
equals the velocity of light. Outside of the horizon, the escape
velocity is less than the speed of light, so if you fire your rockets
hard enough, you can give yourself enough energy to get away. But if
you find yourself inside the horizon, then no matter how powerful your
rockets are, you can't escape.
The horizon has some very strange geometrical properties. To an
observer who is sitting still somewhere far away from the black hole,
the horizon seems to be a nice, static, unmoving spherical surface.
But once you get close to the horizon, you realize that it has a very
large velocity. In fact, it is moving outward at the speed of light!
That explains why it is easy to cross the horizon in the inward
direction, but impossible to get back out. Since the horizon is
moving out at the speed of light, in order to escape back across it,
you would have to travel faster than light. You can't go faster than
light, and so you can't escape from the black hole.
(If all of this sounds very strange, don't worry. It is strange. The
horizon is in a certain sense sitting still, but in another sense it
is flying out at the speed of light. It's a bit like Alice in
"Through the Looking-Glass": she has to run as fast as she can just to
stay in one place.)
Once you're inside of the horizon, spacetime is distorted so much that
the coordinates describing radial distance and time switch roles.
That is, "r", the coordinate that describes how far away you are from
the center, is a timelike coordinate, and "t" is a spacelike one. One
consequence of this is that you can't stop yourself from moving to
smaller and smaller values of r, just as under ordinary circumstances
you can't avoid moving towards the future (that is, towards larger and
larger values of t). Eventually, you're bound to hit the singularity
at r = 0. You might try to avoid it by firing your rockets, but it's
futile: no matter which direction you run, you can't avoid your
future. Trying to avoid the center of a black hole once you've
crossed the horizon is just like trying to avoid next Thursday.
Incidentally, the name 'black hole' was invented by John Archibald
Wheeler, and seems to have stuck because it was much catchier than
previous names. Before Wheeler came along, these objects were often
referred to as 'frozen stars.' I'll explain why below.
TOP
The jet originating from the center
of M87 in this image comes from an active galactic nucleus
that may contain a supermassive black hole.
How big is a black hole?
There are at least two different ways to describe how big something
is. We can say how much mass it has, or we can say how much space it
takes up. Let's talk first about the masses of black holes.
There is no limit in principle to how much or how little mass a black
hole can have. Any amount of mass at all can in principle be made to
form a black hole if you compress it to a high enough density. We
suspect that most of the black holes that are actually out there were
produced in the deaths of massive stars, and so we expect those black
holes to weigh about as much as a massive star. A typical mass for
such a stellar black hole would be about 10 times the mass of the Sun,
or about 10^{31} kilograms. (Here I'm using scientific notation:
10^{31} means a 1 with 31 zeroes after it, or
10,000,000,000,000,000,000,000,000,000,000.) Astronomers also suspect
that many galaxies harbor extremely massive black holes at their
centers. These are thought to weigh about a million times as much as
the Sun, or 10^{36} kilograms.
The more massive a black hole is, the more space it takes up. In
fact, the Schwarzschild radius (which means the radius of the horizon)
and the mass are directly proportional to one another: if one black
hole weighs ten times as much as another, its radius is ten times as
large. A black hole with a mass equal to that of the Sun would have a
radius of 3 kilometers. So a typical 10-solar-mass black hole would
have a radius of 30 kilometers, and a million-solar-mass black hole at
the center of a galaxy would have a radius of 3 million kilometers.
Three million kilometers may sound like a lot, but it's actually not
so big by astronomical standards. The Sun, for example, has a radius
of about 700,000 kilometers, and so that supermassive black hole has a
radius only about four times bigger than the Sun.
TOP
What would happen to me if I fell into a black hole?
Let's suppose that you get into your spaceship and point it straight
towards the million-solar-mass black hole in the center of our galaxy.
(Actually, there's some debate about whether our galaxy contains a
central black hole, but let's assume it does for the moment.)
Starting from a long way away from the black hole, you just turn off
your rockets and coast in. What happens?
At first, you don't feel any gravitational forces at all. Since
you're in free fall, every part of your body and your spaceship is
being pulled in the same way, and so you feel weightless. (This is
exactly the same thing that happens to astronauts in Earth orbit: even
though both astronauts and space shuttle are being pulled by the
Earth's gravity, they don't feel any gravitational force because
everything is being pulled in exactly the same way.) As you get
closer and closer to the center of the hole, though, you start to feel
"tidal" gravitational forces. Imagine that your feet are closer to
the center than your head. The gravitational pull gets stronger as
you get closer to the center of the hole, so your feet feel a stronger
pull than your head does. As a result you feel "stretched." (This
force is called a tidal force because it is exactly like the forces
that cause tides on earth.) These tidal forces get more and more
intense as you get closer to the center, and eventually they will rip
you apart.
For a very large black hole like the one you're falling into, the
tidal forces are not really noticeable until you get within about
600,000 kilometers of the center. Note that this is after you've
crossed the horizon. If you were falling into a smaller black hole,
say one that weighed as much as the Sun, tidal forces would start to
make you quite uncomfortable when you were about 6000 kilometers away
from the center, and you would have been torn apart by them long
before you crossed the horizon. (That's why we decided to let you
jump into a big black hole instead of a small one: we wanted you to
survive at least until you got inside.)
What do you see as you are falling in? Surprisingly, you don't
necessarily see anything particularly interesting. Images of faraway
objects may be distorted in strange ways, since the black hole's
gravity bends light, but that's about it. In particular, nothing
special happens at the moment when you cross the horizon. Even after
you've crossed the horizon, you can still see things on the outside:
after all, the light from the things on the outside can still reach
you. No one on the outside can see you, of course, since the light
from you can't escape past the horizon.
How long does the whole process take? Well, of course, it depends on
how far away you start from. Let's say you start at rest from a point
whose distance from the singularity is ten times the black hole's
radius. Then for a million-solar-mass black hole, it takes you about
8 minutes to reach the horizon. Once you've gotten that far, it takes
you only another seven seconds to hit the singularity. By the way,
this time scales with the size of the black hole, so if you'd jumped
into a smaller black hole, your time of death would be that much
sooner.
Once you've crossed the horizon, in your remaining seven seconds, you
might panic and start to fire your rockets in a desperate attempt to
avoid the singularity. Unfortunately, it's hopeless, since the
singularity lies in your future, and there's no way to avoid your
future. In fact, the harder you fire your rockets, the sooner you hit
the singularity. It's best just to sit back and enjoy the ride.
TOP
My friend Penelope is sitting still at a safe distance, watching me fall into the black hole. What does she see?
Penelope sees things quite differently from you. As you get closer
and closer to the horizon, she sees you move more and more slowly. In
fact, no matter how long she waits, she will never quite see you reach
the horizon.
In fact, more or less the same thing can be said about the material
that formed the black hole in the first place. Suppose that the black
hole formed from a collapsing star. As the material that is to form
the black hole collapses, Penelope sees it get smaller and smaller,
approaching but never quite reaching its Schwarzschild radius. This
is why black holes were originally called frozen stars: because they
seem to 'freeze' at a size just slightly bigger than the Schwarzschild
radius.
Why does she see things this way? The best way to think about it is
that it's really just an optical illusion. It doesn't really take an
infinite amount of time for the black hole to form, and it doesn't
really take an infinite amount of time for you to cross the horizon.
(If you don't believe me, just try jumping in! You'll be across the
horizon in eight minutes, and crushed to death mere seconds later.)
As you get closer and closer to the horizon, the light that you're
emitting takes longer and longer to climb back out to reach Penelope.
In fact, the radiation you emit right as you cross the horizon will
hover right there at the horizon forever and never reach her. You've
long since passed through the horizon, but the light signal telling
her that won't reach her for an infinitely long time.
There is another way to look at this whole business. In a sense, time
really does pass more slowly near the horizon than it does far away.
Suppose you take your spaceship and ride down to a point just outside
the horizon, and then just hover there for a while (burning enormous
amounts of fuel to keep yourself from falling in). Then you fly back
out and rejoin Penelope. You will find that she has aged much more
than you during the whole process; time passed more slowly for you
than it did for her.
So which of these two explanation (the optical-illusion one or the
time-slowing-down one) is really right? The answer depends on what
system of coordinates you use to describe the black hole. According
to the usual system of coordinates, called "Schwarzschild
coordinates," you cross the horizon when the time coordinate t is
infinity. So in these coordinates it really does take you infinite
time to cross the horizon. But the reason for that is that
Schwarzschild coordinates provide a highly distorted view of what's
going on near the horizon. In fact, right at the horizon the
coordinates are infinitely distorted (or, to use the standard
terminology, "singular"). If you choose to use coordinates that are
not singular near the horizon, then you find that the time when you
cross the horizon is indeed finite, but the time when Penelope sees
you cross the horizon is infinite. It took the radiation an infinite
amount of time to reach her. In fact, though, you're allowed to use
either coordinate system, and so both explanations are valid. They're
just different ways of saying the same thing.
In practice, you will actually become invisible to Penelope before too
much time has passed. For one thing, light is "redshifted" to longer
wavelengths as it rises away from the black hole. So if you are
emitting visible light at some particular wavelength, Penelope will
see light at some longer wavelength. The wavelengths get longer and
longer as you get closer and closer to the horizon. Eventually, it
won't be visible light at all: it will be infrared radiation, then
radio waves. At some point the wavelengths will be so long that
she'll be unable to observe them. Furthermore, remember that light is
emitted in individual packets called photons. Suppose you are
emitting photons as you fall past the horizon. At some point, you
will emit your last photon before you cross the horizon. That photon
will reach Penelope at some finite time -- typically less than an hour
for that million-solar-mass black hole -- and after that she'll never
be able to see you again. (After all, none of the photons you emit
*after* you cross the horizon will ever get to her.)
TOP
If a black hole existed, would it suck up all the matter in the
Universe?
Heck, no. A black hole has a "horizon," which means a region from
which you can't escape. If you cross the horizon, you're doomed to
eventually hit the singularity. But as long as you stay outside of
the horizon, you can avoid getting sucked in. In fact, to someone
well outside of the horizon, the gravitational field surrounding a
black hole is no different from the field surrounding any other object
of the same mass. In other words, a one-solar-mass black hole is no
better than any other one-solar-mass object (such as, for example, the
Sun) at "sucking in" distant objects.
TOP
What if the Sun became a black hole?
Well, first, let me assure you that the Sun has no intention of doing
any such thing. Only stars that weigh considerably more than the Sun
end their lives as black holes. The Sun is going to stay roughly the
way it is for another five billion years or so. Then it will go
through a brief phase as a red giant star, during which time it will
expand to engulf the planets Mercury and Venus, and make life quite
uncomfortable on Earth (oceans boiling, atmosphere escaping, that sort
of thing). After that, the Sun will end its life by becoming a boring
white dwarf star. If I were you, I'd make plans to move somewhere far
away before any of this happens. I also wouldn't buy any of those
8-billion-year government bonds.
But I digress. What if the Sun *did* become a black hole for some
reason? The main effect is that it would get very dark and very cold
around here. The Earth and the other planets would not get sucked
into the black hole; they would keep on orbiting in exactly the same
paths they follow right now. Why? Because the horizon of this black
hole would be very small -- only about 3 kilometers -- and as we
observed above, as long as you stay well outside the horizon, a black
hole's gravity is no stronger than that of any other object of the
same mass.
TOP
Is there any evidence that black holes exist?
Yes. You can't see a black hole directly, of course, since light
can't get past the horizon. That means that we have to rely on
indirect evidence that black holes exist.
Suppose you have found a region of space where you think there might
be a black hole. How can you check whether there is one or not? The
first thing you'd like to do is measure how much mass there is in that
region. If you've found a large mass concentrated in a small volume,
and if the mass is dark, then it's a good guess that there's a black
hole there. There are two kinds of systems in which astronomers have
found such compact, massive, dark objects: the centers of galaxies
(including perhaps our own Milky Way Galaxy), and X-ray-emitting
binary systems in our own Galaxy.
According to a recent review by Kormendy and Richstone (to appear in
the 1995 edition of "Annual Reviews of Astronomy and Astrophysics"),
eight galaxies have been observed to contain such massive dark objects
in their centers. The masses of the cores of these galaxies range
from one million to several billion times the mass of the Sun. The
mass is measured by observing the speed with which stars and gas orbit
around the center of the galaxy: the faster the orbital speeds, the
stronger the gravitational force required to hold the stars and gas in
their orbits. (This is the most common way to measure masses in
astronomy. For example, we measure the mass of the Sun by observing
how fast the planets orbit it, and we measure the amount of dark
matter in galaxies by measuring how fast things orbit at the edge of
the galaxy.)
These massive dark objects in galactic centers are thought to be black
holes for at least two reasons. First, it is hard to think of
anything else they could be: they are too dense and dark to be stars
or clusters of stars. Second, the only promising theory to explain
the enigmatic objects known as quasars and active galaxies postulates
that such galaxies have supermassive black holes at their cores. If
this theory is correct, then a large fraction of galaxies -- all the
ones that are now or used to be active galaxies -- must have
supermassive black holes at the center. Taken together, these
arguments strongly suggest that the cores of these galaxies contain
black holes, but they do not constitute absolute proof.
Two very recent discovery has been made that strongly support the
hypothesis that these systems do indeed contain black holes. First, a
nearby active galaxy was found to have a "water maser" system (a very
powerful source of microwave radiation) near its nucleus. Using the
technique of very-long-baseline interferometry, a group of researchers
was able to map the velocity distribution of the gas with very fine
resolution. In fact, they were able to measure the velocity within
less than half a light-year of the center of the galaxy. From this
measurement they can conclude that the massive object at the center of
this galaxy is less than half a light-year in radius. It is hard to
imagine anything other than a black hole that could have so much mass
concentrated in such a small volume. (This result was reported by
Miyoshi et al. in the 12 January 1995 issue of Nature, vol. 373, p.
127.)
A second discovery provides even more compelling evidence. X-ray
astronomers have detected a spectral line from one galactic nucleus
that indicates the presence of atoms near the nucleus that are moving
extremely fast (about 1/3 the speed of light). Furthermore, the
radiation from these atoms has been redshifted in just the manner one
would expect for radiation coming from near the horizon of a black
hole. These observations would be very difficult to explain in any
other way besides a black hole, and if they are verified, then the
hypothesis that some galaxies contain supermassive black holes at
their centers would be fairly secure. (This result was reported in
the 22 June 1995 issue of Nature, vol. 375, p. 659, by Tanaka et al.)
A completely different class of black-hole candidates may be found in
our own Galaxy. These are much lighter, stellar-mass black holes,
which are thought to form when a massive star ends its life in a
supernova explosion. If such a stellar black hole were to be off
somewhere by itself, we wouldn't have much hope of finding it.
However, many stars come in binary systems -- pairs of stars in orbit
around each other. If one of the stars in such a binary system
becomes a black hole, we might be able to detect it. In particular,
in some binary systems containing a compact object such as a black
hole, matter is sucked off of the other object and forms an "accretion
disk" of stuff swirling into the black hole. The matter in the
accretion disk gets very hot as it falls closer and closer to the
black hole, and it emits copious amounts of radiation, mostly in the
X-ray part of the spectrum. Many such "X-ray binary systems" are
known, and some of them are thought to be likely black-hole
candidates.
Suppose you've found an X-ray binary system. How can you tell whether
the unseen compact object is a black hole? Well, one thing you'd
certainly like to do is to estimate its mass. By measuring the
orbital speed of visible star (together with a few other things), you
can figure out the mass of the invisible companion. (The technique is
quite similar to the one we described above for supermassive black
holes in galactic centers: the faster the star is moving, the stronger
the gravitational force required to keep it in place, and so the more
massive the invisible companion.) If the mass of the compact object
is found to be very large very large, then there is no kind of object
we know about that it could be other than a black hole. (An ordinary
star of that mass would be visible. A stellar remnant such as a
neutron star would be unable to support itself against gravity, and
would collapse to a black hole.) The combination of such mass
estimates and detailed studies of the radiation from the accretion
disk can supply powerful circumstantial evidence that the object in
question is indeed a black hole.
Many of these "X-ray binary" systems are known, and in some cases the
evidence in support of the black-hole hypothesis is quite strong. In
a review article in the 1992 issue of Annual Reviews of Astronomy and
Astrophysics, Anne Cowley summarized the situation by saying that
there were three such systems known (two in our galaxy and one in the
nearby Large Magellanic Cloud) for which very strong evidence exists
that the mass of the invisible object is too large to be anything but
a black hole. There are many more such objects that are thought to be
likely black holes on the basis of slightly less evidence.
Furthermore, this field of research has been very active since 1992,
and the number of strong candidates by now is larger than three.
TOP
How do black holes evaporate?
This is a tough one. Back in the 1970's, Stephen Hawking came up with
theoretical arguments showing that black holes are not really entirely
black: due to quantum-mechanical effects, they emit radiation. The
energy that produces the radiation comes from the mass of the black
hole. Consequently, the black hole gradually shrinks. It turns out
that the rate of radiation increases as the mass decreases, so the
black hole continues to radiate more and more intensely and to shrink
more and more rapidly until it presumably vanishes entirely.
Actually, nobody is really sure what happens at the last stages of
black hole evaporation: some researchers think that a tiny, stable
remnant is left behind. Our current theories simply aren't good
enough to let us tell for sure one way or the other. As long as I'm
disclaiming, let me add that the entire subject of black hole
evaporation is extremely speculative. It involves figuring out how to
perform quantum-mechanical (or rather quantum-field-theoretic)
calculations in curved spacetime, which is a very difficult task, and
which gives results that are essentially impossible to test with
experiments. Physicists *think* that we have the correct theories to
make predictions about black hole evaporation, but without
experimental tests it's impossible to be sure.
Now why do black holes evaporate? Here's one way to look at it, which
is only moderately inaccurate. (I don't think it's possible to do
much better than this, unless you want to spend a few years learning
about quantum field theory in curved space.) One of the consequences
of the uncertainty principle of quantum mechanics is that it's
possible for the law of energy conservation to be violated, but only
for very short durations. The Universe is able to produce mass and
energy out of nowhere, but only if that mass and energy disappear
again very quickly. One particular way in which this strange
phenomenon manifests itself goes by the name of vacuum fluctuations.
Pairs consisting of a particle and antiparticle can appear out of
nowhere, exist for a very short time, and then annihilate each other.
Energy conservation is violated when the particles are created, but
all of that energy is restored when they annihilate again. As weird
as all of this sounds, we have actually confirmed experimentally that
these vacuum fluctuations are real.
Now, suppose one of these vacuum fluctuations happens near the horizon
of a black hole. It may happen that one of the two particles falls
across the horizon, while the other one escapes. The one that escapes
carries energy away from the black hole and may be detected by some
observer far away. To that observer, it will look like the black hole
has just emitted a particle. This process happens repeatedly, and the
observer sees a continuous stream of radiation from the black hole.
TOP
Won't the black hole have evaporated out from under me before I reach it?
We've observed that, from the point of view of your friend Penelope
who remains safely outside of the black hole, it takes you an infinite
amount of time to cross the horizon. We've also observed that black
holes evaporate via Hawking radiation in a finite amount of time. So
by the time you reach the horizon, the black hole will be gone, right?
Wrong. When we said that Penelope would see it take forever for you
to cross the horizon, we were imagining a non-evaporating black hole.
If the black hole is evaporating, that changes things. Your friend
will see you cross the horizon at the exact same moment she sees the
black hole evaporate. Let me try to describe why this is true.
Remember what we said before: Penelope is the victim of an optical
illusion. The light that you emit when you're very near the horizon
(but still on the outside) takes a very long time to climb out and
reach her. If the black hole lasts forever, then the light may take
arbitrarily long to get out, and that's why she doesn't see you cross
the horizon for a very long (even an infinite) time. But once the
black hole has evaporated, there's nothing to stop the light that
carries the news that you're about to cross the horizon from reaching
her. In fact, it reaches her at the same moment as that last burst of
Hawking radiation. Of course, none of that will matter to you: you've
long since crossed the horizon and been crushed at the singularity.
Sorry about that, but you should have thought about it before you
jumped in.
TOP
What is a white hole?
The equations of general relativity have an interesting mathematical
property: they are symmetric in time. That means that you can take
any solution to the equations and imagine that time flows backwards
rather than forwards, and you'll get another valid solution to the
equations. If you apply this rule to the solution that describes
black holes, you get an object known as a white hole. Since a black
hole is a region of space from which nothing can escape, the
time-reversed version of a black hole is a region of space into which
nothing can fall. In fact, just as a black hole can only suck things
in, a white hole can only spit things out.
White holes are a perfectly valid mathematical solution to the
equations of general relativity, but that doesn't mean that they
actually exist in nature. In fact, they almost certainly do not
exist, since there's no way to produce one. (Producing a white hole
is just as impossible as destroying a black hole, since the two
processes are time-reversals of each other.)
TOP
What is a wormhole?
 So far, we have only considered ordinary "vanilla" black holes.
Specifically, we have been talking all along about black holes that
are not rotating and have no electric charge. If we consider black
holes that rotate and/or have charge, things get more complicated. In
particular, it is possible to fall into such a black hole and not hit
the singularity. In effect, the interior of a charged or rotating
black hole can "join up" with a corresponding white hole in such a way
that you can fall into the black hole and pop out of the white hole.
This combination of black and white holes is called a wormhole.
The white hole may be somewhere very far away from the black hole;
indeed, it may even be in a "different Universe" -- that is, a region
of spacetime that, aside from the wormhole itself, is completely
disconnected from our own region. A conveniently-located wormhole
would therefore provide a convenient and rapid way to travel very
large distances, or even to travel to another Universe. Maybe the
exit to the wormhole would lie in the past, so that you could travel
back in time by going through. All in all, they sound pretty cool.
But before you apply for that research grant to go search for them,
there are a couple of things you should know. First of all, wormholes
almost certainly do not exist. As we said above in the section on
white holes, just because something is a valid mathematical solution
to the equations doesn't mean that it actually exists in nature. In
particular, black holes that form from the collapse of ordinary matter
(which includes all of the black holes that we think exist) do not
form wormholes. If you fall into one of those, you're not going to
pop out anywhere. You're going to hit a singularity, and that's all
there is to it.
Furthermore, even if a wormhole were formed, it is thought that it
would not be stable. Even the slightest perturbation (including the
perturbation caused by your attempt to travel through it) would cause
it to collapse.
Finally, even if wormholes exist and are stable, they are quite
unpleasant to travel through. Radiation that pours into the wormhole
(from nearby stars, the cosmic microwave background, etc.) gets
blueshifted to very high frequencies. As you try to pass through the
wormhole, you will get fried by these X-rays and gamma rays.
TOP
Where can I go to learn more about black holes?
Let me begin by acknowledging that I cribbed some of the above
material from the article about black holes in the Frequently Asked
Questions list for the Usenet newsgroup sci.physics. The sci.physics
FAQ is posted monthly to sci.physics and is also available by
anonymous ftp from rtfm.mit.edu (and probably other places). The
article about black holes, which is excellent, was written by Matt
McIrvin. The FAQ contains other neat things too.
There are lots of books out there about black holes and related
matters. Kip Thorne's "Black Holes and Time Warps: Einstein's
Outrageous Legacy" is a good one. William Kaufmann's "Black Holes and
Warped Spacetime" is also worth reading. R. Wald's "Space, Time, and
Gravity" is an exposition of general relativity for non-scientists. I
haven't read it myself, but I've heard good things about it.
Both of these books are aimed at readers without much background in
physics. If you want more "meat" (i.e., more mathematics), then you
probably start with a book on the basics of relativity theory. The
best introduction to the subject is "Spacetime Physics" by E.F. Taylor
and J.A. Wheeler. (This book is mostly about special relativity, but
the last chapter discusses the general theory.) Taylor and Wheeler
have been threatening for about two years now to publish a sequel
entitled "Scouting Black Holes," which should be quite good if it ever
comes out. "Spacetime Physics" does not assume that you know vast
amounts of physics, but it does assume that you're willing to work
hard at understanding this stuff. It is not light reading, although
it is more playful and less intimidating than most physics books.
Finally, if "Spacetime Physics" isn't enough for you, you could try
any of several introductions to general relativity. B. Schutz's "A
First Course in General Relativity" and W. Rindler's "Essential
Relativity" are a couple of possibilities. And for the extremely
valiant reader with an excellent background in physics, there's the
granddaddy of all books on general relativity, Misner, Thorne, and
Wheeler's "Gravitation." R. Wald's book "General Relativity" is at a
comparable level to "Gravitation," although the styles of the two
books are enormously different. What little I know about black-hole
evaporation comes from Wald's book. Let me emphasize that all of
these books, and especially the last two, assume that you know quite a
lot of physics. They are not for the faint of heart.
TOP
September 1995
Singularity Home •
Black Hole Buyer's
Guide • Black Hole FAQ
|
