Frontiers and Controversies in Astrophysics: Lecture 9 Transcript
February 15, 2007
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Professor Charles Bailyn:
Okay, let's startlet's see, we started talking about black holes last time, and
there's now going to be a problem set that is going to be available later today, due next week. And I should
also point that I've put together this website on black holes. Actually, some of the help sheets already send
you to that website. And I'll put a link on the classes server as a whole, but here it is as an actual URL,
cmi.yale.edu/bh
for black holes. And that website kind of serves as a sort of online textbook for this part of
the course. And so, you have something written down to look at for this whole section of the course. And, as
you'll see, many of the things we'll be talking about are actually discussed on that website, as well. So, you
can find out more information there.
Okay, so Ilast time, I defined a black hole. This is simply something where the escape velocity is faster than
the speed of light. Or, alternatively, and this isamounts to the exact same thing, the radius of the object is
less than the Schwarzschild radius, which is defined for an object of any given mass. And this isn't
particularly extraordinary or interesting, as long as the speed of light isn't particularly extraordinary or
interesting. And one of the things that happens when you start talking about relativity is that it turns out the
speed of light is a very important quantity. So thisthese are interesting because the speed of light is
interesting.
And, we'll talk in a minute about how all this arises, but one of the interesting things about the speed of light
is that you can't go any faster. It's the speed limit, and no physical process can make you go faster than the
speed of light. So,
c
is fastest velocity possible. And the consequence of that is, supposing you have one of
these black hole thingsso, here's some object, and it's got some radius. And its radius and its mass are such
that the escape velocity, here, is greater than the speed of light. You could imagine that around it is a kind of
imaginary sphere. Let's put it in dots. And this is the sphere where the escape velocity is equal to the speed of
light. And you remember what the formula for the escape velocity
V
esc
is equal to 2
GM
/
R
, the square root
of 2
GM
/
R
.
And so, if on the surface of this object, the escape velocity is greater than that of light, if you keep moving
out,
R
will keep getting bigger. And so, eventually you'll come to a point in space where the escape velocity
is equal to the speed of light, and this is called the event horizon. And the reason it's called that is because, if
nothing can go faster than the speed of light, what it means is that any event that takes place inside this
imaginary sphere can't radiate any information about what's going on to the outside, because thisthe escape
velocity's greater than the speed of light. Light can't escape, and because nothing else can go faster than the
speed of light, nothing else can escape. And so, no information of any kind can comecomes from inside the
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 Spring '06
 CharlesBailyn
 Black Holes, General Relativity, The Time Machine, event horizon, Professor Charles Bailyn

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