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Astronomy 309R – Spring 2009
Study Guide to help prepare for Exam 4
Please read chapters 9, 10, and 11 in Hawley & Holcomb.
Chapter 11 is more mathematically
advanced than we need for this course, but please do read it carefully nonetheless.
Also, please
do review the lecture slides on black holes and the expansion of the universe in the Blackboard.
Particularly general and important concepts are underlined.
Black Holes
Explain the event horizon of a black hole.
Is the event horizon a material surface, like that of a
star or a planet?
(The event horizon is not a material surface, but an imaginary, geometrical
surface around the center of the black hole.)
Write down the formula that relates the
Schwarzschild radius to the mass of a black hole.
The Schwarzschild radius equals the radius of
the event horizon when the black hole does not rotate; the event horizon of a rotating black hole
is slightly smaller than that of a nonrotating black hole.
How can we relate the Schwarzschild
radius to the escape velocity?
[The Schwarzschild radius coincides with the radius where the
escape velocity equals the speed of light.
Square of the escape velocity at distance
R
from a
body of mass
M
equals (
V
escape
)
2
= 2 G M / R.
When
R
equals the Schwarzschild radius, the
escape velocity equals the speed of light.]
What happens to the “strength of gravity,” as we have
defined in lecture, as one approaches the event horizon of a black hole?
Imagine that from a distance, we are watching a light source fall into a black hole.
As the source
approaches the event horizon, would it appear redder of bluer than it really is?
(Please consider
the gravitational redshift or blueshift form the lecture on general relativity.)
Consider a clock
approaching the event horizon of a black hole.
Does the clock appear fast or slow?
How could an observer inside a rocket notice that they are falling into a black hole?
(The tidal
gravitational field is strong; the observer’s body will be stretched head from toe.)
Consider a person falling into a black hole.
At the moment that the person passes the event
horizon, the person’s entire future (all the events that can be causally influenced by the person) is
contained inside the black hole.
The observer’s entire past (all events that that can causally
influence the person) is contained outside the black hole.
At the moment of passing the event
horizon, the person sees only the world outside the black hole, but not the world inside the black
hole.
Consider a spaceship that uses its rocket engines to fly around a black hole just outside the event
horizon. What can be said about the velocity of the spaceship?
(The closer to the black hole that
a rocket tries to orbit, the higher the rocket’s velocity must be.
Just outside the black hole’s
horizon, the rocket’s velocity must be close to the speed of light.)
What are the two sizes in which black holes appear in the universe?
(Astronomical black holes
have been found with masses between about 5 and 15 solar masses—these are the “stellarsized”
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 Spring '08
 JohnLacy
 Astronomy, Black Holes, General Relativity, Black hole

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