Hi again everyone! I’m hoping you’re enjoying
our stroll through all sorts of fascinating
black hole related topics. There are a couple
more topics we can cover, including one where,
over cosmic time scales, black holes can evaporate
into nothingness. This mind-bending phenomenon
is the topic of this week’s episode of Subatomic
Stories.
One of the commonly held features of black
holes is that they suck things in and nothing
can escape. That seems familiar enough, but
in the 1970s Stephen Hawking tried to combine
quantum thinking with black holes and found
that this wasn’t exactly true. Hawking claimed
that black holes could emit radiation that
we now call Hawking radiation.
There are a number of ways to visualize how
Hawking radiation works, but a simple mental
image is my favorite. Basically, the idea
is that all of space is full of virtual particles
appearing and disappearing. I talked about
this in episode nine of this series. If these
virtual particles are appearing and disappearing
in the vicinity of the event horizon of a
black hole, they will be created temporarily
with a little momentum, and the momentum will
be in opposite directions. This momentum will
kick one particle down below the event horizon
and the other will be kicked away to escape.
The escaping particle will carry away the
energy and reduce the mass of the black hole.
Now, there are some common reactions to this
explanation. The first is some people will
ask how this reduces the black hole’s mass.
After all, I just said that it absorbed a
particle. The answer to this is that you have
to think of the black hole as not just the
singularity, but the entire product, from
the singularity, to the event horizon, to
the distortion of space surrounding the horizon-
the whole enchilada.
When a particle escapes the vicinity of the
black hole, some of the overall energy is
lost. The particle that falls into the hole
was already there and part of the hole’s
energy. It just moved from one place to the
other.
If black holes radiate energy, then they must
have a temperature. The temperature for a
non-rotating, electrically neutral, black
hole is equal to 6 times ten to the minus
eight kelvin, divided by the mass of the black
hole in units of solar mass. For example,
for a black hole with ten times the mass of
the sun, you’d divide that number by ten.
That’s a crazy small temperature. The temperature
of space is 2.7 kelvin, which is remnant temperature
of the Big Bang. That means that black holes
will absorb more energy from space than they
emit. That will be true for a long time, but
eventually the expanding universe will drop
the temperature of space to below the temperature
of black holes. At that temperature, which
will of course depend on the individual black
hole, they will emit more radiation than they
absorb.
If an object emits more energy than it absorbs,
it'll lose energy. And, since E equals m c
squared, that means that the black hole will
lose mass. Now, it will lose mass slowly.
In fact, we can calculate the lifetime of
a black hole. It is about ten to the 74 seconds
times the mass of the black hole in units
of the mass of the sun cubed. If you prefer
the number in units of years, that’s about
ten to the 67 times the cube of the mass of
the black hole in solar units.
To give you a sense of scale, the lifetime
of the universe so far is only ten to the
ten years. So, it’s going to take a long
time for black holes to evaporate. But, evaporate
they will. Assuming that nothing unexpected
happens as the universe evolves, eventually
the stars will burn out and clump together
in ginormous black holes. The black holes
will then slowly evaporate away and the universe
will consist of nothing but photons from the
evaporation of black holes.
But it’s going to take a long time, so you
still have to do your homework, paint your
shed, mow your lawn, or whatever it is you’re
avoiding.
By the way, the mental picture I painted of
how Hawking radiation works is useful, but
it isn’t the most accurate one. A more accurate
version involves some very interesting effects.
One is called the Unruh effect. In the Unruh
effect, accelerating observers see the world
differently than non-accelerating ones. Accelerating
observers can see particles in patches of
space where non-accelerating observers see
nothing.
And an object near the event horizon of a
black hole will need to accelerate to avoid
falling in and this is the more nuanced explanation
of the origin of Hawking radiation. I’ve
put a link in the video description to the
more detailed explanation. It’s pretty tricky
and I put it there if you're truly curious.
But you know what can also be tricky? Viewer’s
questions, that’s what. Sometimes they can
be pretty hard. So, let’s go see what surprises
our viewers have for us this week.
It’s question time, and boy, there were
some doozies. I’d love to have answered
more, but there were just too many good ones.
So I picked a couple that many of you asked.
Let’s get started.
A number of you came up with clever ways to
pronounce my name, but a comment by Neither
a theorem nor celery got my attention. There’s
got to be quite a story behind that YouTube
handle, but I digress.
Neither noted that my first name is pronounced
the same in all languages. I suppose that
could be true, but I do have a funny story
to relate about that. I was giving a series
of lectures in Medellin, Colombia and I was
assigned a student by the name of Sebastian
to babysit me and make sure I stayed out of
trouble. Amazing guy, by the way. He took
me here and there and introduced me to a great
number of people.
We got to be friendly and chatted quite freely.
Towards the end he mentioned that it was sometimes
awkward to introduce me because, in Spanish,
the word “Don” is an honorific- kind of
like Don Corleone in the Godfather. I didn’t
really warrant the title, after all I’m
just a friendly neighborhood physicist. But
I’m sure some people got the wrong impression
and I didn’t have a clue. That’s one of
my many name mix up stories from my travels.
Okay. Moving on.
K- hah, a name I can pronounce right- asked
why gravitational waves drop off linearly,
rather than as the square of the distance.
Hi K. Excellent question, with an unfortunately
complicated answer. It comes down to the kinds
of motions that cause gravitational waves
compared to electromagnetic ones. In EM waves,
if you have two charges of opposite sign and
you move them away or towards one another,
it will generate radiation of a form called
dipole radiation.
Dipole radiation decreases in intensity as
the distance squared. But gravity doesn’t
emit dipole radiation. If you take two objects
and separate them, conservation of momentum,
energy, and angular momentum forbids dipole
radiation. Only certain types of motion will
emit radiation and the simplest is when two
masses orbit one another. This kind of radiation
is called quadrupole radiation and the amplitude
falls off linearly as the distance. This is
just a property of quadrupole radiation.
There is a lot more to say about this, and
I put a URL in the video description pointing
to a nice article by Ethan Siegel on the topic.
Plus it has some very nice animated gifs that
are totally worth your time to look at. Check
it out if you are interested.
Zoltan asks what a person falling into a black
hole will see of the surrounding universe.
Hi Zoltan. Such a person will see the opposite
of what an outsider looking in sees. The person
falling into a black hole will see their clock
looks unchanged, but distant clocks will speed
up and appear bluer and bluer. But that spaghettification
will still be a problem.
Speaking of spaghetti, the internationally
renowned philosopher Samuel Machado ponders
what happens if spaghetti falls into a black
hole. Well, since spaghettification makes
things longer and skinnier, I think the spaghetti
would turn into angel hair pasta. Sounds reasonable
to me. And yummy. What do you think?
Bbbf09 also addresses a spaghettification
topic. He or she notes that spaghettification
doesn’t happen near supermassive black holes.
Hi BB. Yes that’s right. Let me explain
to the viewers why.
Spaghettification occurs not because of strong
gravity, but because the gravity is different
in two different locations. Let’s start
with two objects, both a kilogram in mass,
separated by a meter.
Let’s look at two black holes- one with
a mass of five solar masses, like a smallish
black hole created from the collapse of a
star and another black hole the size of the
huge monster lurking at the center of the
Milky Way, with a mass of about four million
solar masses. Way bigger. By the way, I’ll
talk about these black hole heavyweights in
an upcoming episode.
The Schwarzschild radius of a small black
hole is 9 miles or 15 kilometers. The Schwarzschild
radius of a monster black hole is 7.3 million
miles or about 11.7 million kilometers. Now
let’s ask what the gravity is for both black
holes, say fifteen thousand meters above the
event horizon. You’re going to be surprised.
By the way, these pictures aren’t to scale.
Near the stellar mass black hole, the gravity
at that distance gives a one kilogram object
that weighs 2.2 pounds on the Earth’s surface
a weight of 34 billion pounds. And the object
a meter further away has a force that is 2.3
million pounds less. So the difference in
gravity pulls the two objects apart with a
force equivalent to 23 million pounds. That’s
where the spaghettification thing comes from.
Now let’s do the same thing with the supermassive
black hole. We’ll put two weights, one 15,000
meters above the event horizon and one 15,001
above it. The close object, which has a mass
of a kilogram, experiences a weight of about
0.2 pounds. And the object a meter farther
away experiences a weight that is only thirty
six trillionths of a pound less. So the two
weights are roughly the same and no spaghettification
occurs. So, yep. Spaghettification is only
for solar mass black holes. I guess it's smaller.
And, finally, in the best approximation tradition
of introductory physics, Valdagast tells us
that the gravitational potential for a spherical,
non-rotating cow is given by the Schwarzschild
mootric. Hi Valdagast. That was a horrible
pun. Truly awful. You should be ashamed. So
first let me salute you. And then, I think
you deserve more recognition, best demonstrated
by two insightful lads by the name of Wayne
and Garth.
We're not worthy! We're not worthy!
Okay, on that respectful note, I think we
need to wrap up this episode. Thanks for all
the questions and sorry if I didn’t get
to yours. There were just too many good ones.
As always, please like, subscribe and share
and always remember the timeless motto of
this video series. “Even at home, physics
is everything.”
