Notes on Relativity and Cosmology - Physics Department, UCSB

280 CHAPTER 9. BLACK HOLES
r = R s
r = R s
Sketch a worldline on this diagram describing you falling into the
black hole as described above.
(b) Suppose that you send out light rays at regular intervals to signal
the rocket. Draw several of these light rays on your diagram.
(c) The people on the rocket watch the light rays you send out through
a telescope. Describe what they see. Do they see you age slowly or
quickly? When do they see you cross the horizon? If they first sit
and watch for awhile, is it possible for them to come and rescue you?
(d) Describe what you feel as you fall in. Is there a difference between
falling into a ‘large’ black hole and a ‘small’ black hole? If so, explain
what it is. [Hint: Have you read section 9.4 on tidal forces yet?]
(e) Suppose now that the rocket sends out light rays toward you at regular
intervals. Describe what you see if you watch these light rays
through a telescope. Do you see people in the rocket age slowly or
quickly? Do you see anything special when you cross the horizon?
Is there a difference between falling into a ‘large’ black hole and a
‘small’ black hole? If so, explain what it is.
For each of the problems below, the term ‘black hole’ refers to the round
Schwarzschild black hole that we have been studying in class.
5. Use your knowledge of static observers in a gravitational field to answer
the following questions.
(a) Is it possible for a rocket to remain static (i.e., to remain at constant
r, θ, φ) at the photon sphere?
(b) If you were placed in such a rocket, would you remain alive? (Hint:
How heavy would you feel?) If the answer depends on the black