Black holes aren’t totally black, and other insights from Stephen Hawking’s groundbreaking work

Black holes aren't totally black, and other insights from Stephen Hawking's groundbreaking work
Credit: NASA Goddard, CC BY

Mathematical physicist and cosmologist Stephen Hawking was
best known for his work exploring the relationship between
black holes and quantum physics. A black hole is the remnant
of a dying supermassive star that’s fallen into itself; these
remnants contract to such a small size that gravity is so
strong even light cannot escape from them. Black holes loom
large in the popular imagination – schoolchildren ponder why
the whole universe doesn’t collapse into one. But Hawking’s
careful theoretical work filled in some of the holes in
physicists’ knowledge about black holes.


Why do black holes exist?

The short answer is: Because gravity exists, and the speed of
light is not infinite.

Imagine you stand on Earth’s surface, and fire a bullet into
the air at an angle. Your standard bullet will come back down,
someplace farther away. Suppose you have a very powerful rifle.
Then you may be able to shoot the bullet at such a speed that,
rather than coming down far away, it will instead “miss” the
Earth. Continually falling, and continually missing the
surface, the bullet will actually be in an orbit around Earth.
If your rifle is even stronger, the bullet may be so fast that
it leaves Earth’s gravity altogether. This is essentially what
happens when we send rockets to Mars, for example.

Now imagine that gravity is much, much stronger. No rifle could
accelerate bullets enough to leave that planet, so instead you
decide to shoot light. While photons (the particles of light)
do not have mass, they are still influenced by gravity, bending
their path just as a bullet’s trajectory is bent by gravity.
Even the heaviest of planets won’t have gravity strong enough
to bend the ‘s path enough to prevent it from
escaping.

But are not like planets or stars,
they are the remnants of stars, packed into the smallest of
spheres, say, just a few kilometers in radius. Imagine you
could stand on the surface of a black hole, armed with your ray
gun. You shoot upwards at an angle and notice that the light
ray instead curves, comes down and misses the surface! Now the
ray is in an “orbit” around the black hole, at a distance
roughly what cosmologists call the Schwarzschild radius, the
“point of no return.”

Thus, as not even light can escape from where you stand, the
object you inhabit (if you could) would look completely black
to someone looking at it from far away: a black hole.

But Hawking discovered that black holes aren’t completely
black?

The short answer is: Yes.

No light can be seen coming from a black hole outside the
Schwarzschild radius. Credit: SubstituteR, CC BY-SA

My previous description of black holes used the language of
classical physics – basically, Newton’s theory applied to
light. But the laws of physics are actually more complicated
because the universe is more complicated.

In classical physics, the word “vacuum” means the total and
complete absence of any form of matter or radiation. But in
quantum physics, the vacuum is much more interesting, in
particular when it is near a black hole. Rather than being
empty, the vacuum is teeming with particle-antiparticle pairs
that are created fleetingly by the vacuum’s energy, but must
annihilate each other shortly thereafter and return their
energy to the vacuum.

You will find all kinds of particle-antiparticle pairs
produced, but the heavier ones occur much more rarely. It’s
easiest to produce photon pairs because they have no mass. The
photons must always be produced in pairs so they’re moving away
from each other and don’t violate the law of momentum
conservation.

Now imagine that a pair is created just at that distance from
the center of the black hole where the “last light ray” is
circulating: the Schwarzschild radius. This distance could be
far from the surface or close, depending on how much mass the
black hole has. And imagine that the is created so that one of the two is
pointing inward – toward you, at the center of the black hole,
holding your ray gun. The other photon is pointing outward. (By
the way, you’d likely be crushed by gravity if you tried this
maneuver, but let’s assume you’re superhuman.)

Now there’s a problem: The one photon that moved inside the
black hole cannot come back out, because it’s already moving at
the speed of light. The photon pair cannot annihilate each
other again and pay back their energy to the vacuum that
surrounds the black hole. But somebody must pay the piper and
this will have to be the black hole itself. After it has
welcomed the photon into its land of no return, the black hole
must return some of its mass back to the universe: the exact
same amount of mass as the energy the pair of photons
“borrowed,” according to Einstein’s famous equality E=mc².

This is essentially what Hawking showed mathematically. The
photon that is leaving the black hole horizon will make it look
as if the black hole had a faint glow: the Hawking radiation
named after him. At the same time he reasoned that if this
happens a lot, for a long time, the black hole might lose so
much mass that it could disappear altogether (or more
precisely, become visible again).

Do black holes make information disappear forever?

Short answer: No, that would be against the law.

Many physicists began worrying about this question shortly
after Hawking’s discovery of the glow. The concern is this: The
fundamental laws of physics guarantee that every process that
happens “forward in time,” can also happen “backwards in time.”

A pair of photons that annihilate each other is labeled A. In
a second pair of photons, labeled B, one enters the black
hole while the other heads outward, setting up an energy debt
that is paid by the black hole. Credit: Christoph Adami, CC
BY-ND

This seems counter to our intuition, where a melon that
splattered on the floor would never magically reassemble
itself. But what happens to big objects like melons is really
dictated by the laws of statistics. For the melon to reassemble
itself, many gazillions of atomic particles would have to do
the same thing backwards, and the likelihood of that is
essentially zero. But for a single particle this is no problem
at all. So for atomic things, everything you observe forwards
could just as likely occur backwards.

Now imagine that you shoot one of two photons into the black
hole. They only differ by a marker that we can measure, but
that does not affect the energy of the photon (this is called a
“polarization”). Let’s call these “left photons” or “right
photons.” After the left or right photon crosses the horizon,
the black hole changes (it now has more energy), but it changes
in the same way whether the left or right photon was absorbed.

Two different histories now have become one future, and such a
future cannot be reversed: How would the laws of physics know
which of the two pasts to choose? Left or right? That is the
violation of time-reversal invariance. The law requires that
every past must have exactly one future, and every future
exactly one past.

Some physicists thought that maybe the Hawking radiation
carries an imprint of left/right so as to give an outside
observer a hint at what the past was, but no. The Hawking
radiation comes from that flickering vacuum surrounding the
black hole, and has nothing to do with what you throw in. All
seems lost, but not so fast.

In 1917, Albert Einstein showed that matter (even the vacuum
next to matter) actually does react to incoming stuff, in a
very peculiar way. The vacuum next to that matter is “tickled”
to produce a particle-antiparticle pair that looks like an
exact copy of what just came in. In a very real sense, the
incoming particle stimulates the matter to create a pair of
copies of itself – actually a copy and an anti-copy. Remember,
random pairs of particle and antiparticle are created in the
all the time, but the tickled-pairs are
not random at all: They look just like the tickler.

This copy process is known as the “stimulated emission” effect
and is at the origin of all lasers. The Hawking glow of black
holes, on the other hand, is just what Einstein called the
“spontaneous emission” effect, taking place near a black hole.

Now imagine that the tickling creates this copy, so that the
left photon tickles a left photon pair, and a right photon
gives a right photon pair. Since one partner of the tickled
pairs must stay outside the black hole (again from momentum
conservation), that particle creates the “memory” that is
needed so that information is preserved: One past has only one
future, time can be reversed, and the laws of physics are safe.

In a cosmic accident, Hawking died on the birthday of Einstein,
whose theory of light, it just so happens, saves Hawking’s
theory of black holes.

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