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.”