COSMIC PERSPECTIVE LL FD
9th Edition
ISBN: 9780135877074
Author: Bennett
Publisher: PEARSON
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Chapter S4, Problem 57EAP
To determine
To Compare:Lifetime of a mini black hole with the age of universe.
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The following quotation is taken from the article “Quantum Black Holes”, by Bernard J. Carr and Steven B. Giddings, in the
May 2005 issue of Scientific American. "The total time for a black hole to evaporate away is proportional to the cube of its
initial mass. For a solar-mass hole, the lifetime is an unobservably long 1064 years."
a. Recall that the solar mass is 2 × 10³0 kilograms. Write a formula for the lifetime, L, of a black hole as a function of its
mass, m. Start by finding the value of the constant k, then write your function using the letter k (rather than its value in
scientific notation). For example, for a direct variation you would write “L(m) = km”.
k = a × 10¹ where a =
L(m) =
b. The present age
mass = c × 10ª kg, where c =
A
and b =
=
of the universe is about 10¹0 years. What would be the mass of a black hole as old as the universe?
ID
and d
=
J
Name:
Hubble Distances
Redshift z parameter
The relativistic redshift is parametrized by z and given by
Δ
In terms of the scale factor,
2=
X
do - de
de
1+z=
ao
a
(2)
Problem 01. Find the redshift z for a Hydrogen spectral line originally at 656 nm which
has been observed at a wavelength of 1.64 μm.
Astro 001 Fall 2022
Problem 02. How much smaller was the universe when this light was emitted?
U₁ = DHO
Using the redshift to measure the velocity, we find
D~
(1)
0.1 Hubble's Law
Hubble's Law states that the recession velocity of a redshifted galaxy is given by the product
of the distance and the Hubble constant.
(3)
ZC
Ho
where c = 3 x 108 m/s and Ho = 2.3 x 10-18 s in standard units. The standard measurement
of the Hubble constant is Ho = 71 (km/s)/Mpc.
Problem 03. What is the distance in Mpc and ly to the galaxy measured in problem 01?
1 pc = 3.26 ly.
A2. A light beam falls radially inwards towards the center of a black hole. First
it passes shell A at a distance rA from the center of the black hole.
It then passes the shell B at a distance rB from the center of the black
the hole. We call the two shell passes event A and event B. Where
large is the time interval between these two events and how can
did you figure it out? Explain with a maximum of 3 sentences (plus any equations
if you wish).
Chapter S4 Solutions
COSMIC PERSPECTIVE LL FD
Ch. S4 - Prob. 1EAPCh. S4 - Prob. 2EAPCh. S4 - Prob. 3EAPCh. S4 - Prob. 4EAPCh. S4 - Prob. 5EAPCh. S4 - Prob. 6EAPCh. S4 - Prob. 7EAPCh. S4 - Prob. 8EAPCh. S4 - Prob. 9EAPCh. S4 - Prob. 10EAP
Ch. S4 - Prob. 11EAPCh. S4 - Prob. 12EAPCh. S4 - Prob. 13EAPCh. S4 - Prob. 14EAPCh. S4 - Prob. 15EAPCh. S4 - Prob. 16EAPCh. S4 - Prob. 17EAPCh. S4 - Prob. 18EAPCh. S4 - Prob. 19EAPCh. S4 - Decide whether the statement makes sense (or is...Ch. S4 - Prob. 21EAPCh. S4 - Prob. 22EAPCh. S4 - Prob. 23EAPCh. S4 - Prob. 24EAPCh. S4 - Prob. 25EAPCh. S4 - Prob. 26EAPCh. S4 - Prob. 27EAPCh. S4 - Choose the best answer to each of the following....Ch. S4 - Prob. 29EAPCh. S4 - Prob. 30EAPCh. S4 - Prob. 31EAPCh. S4 - Prob. 32EAPCh. S4 - Prob. 33EAPCh. S4 - Prob. 34EAPCh. S4 - Prob. 36EAPCh. S4 - Prob. 37EAPCh. S4 - Prob. 38EAPCh. S4 - Prob. 39EAPCh. S4 - Prob. 41EAPCh. S4 - Prob. 42EAPCh. S4 - Prob. 43EAPCh. S4 - Prob. 44EAPCh. S4 - Prob. 45EAPCh. S4 - Prob. 46EAPCh. S4 - Prob. 47EAPCh. S4 - Prob. 48EAPCh. S4 - Prob. 52EAPCh. S4 - Large-Scale Gravity. Suppose Earth and the Sun...Ch. S4 - Prob. 54EAPCh. S4 - Solar Mass Black Holes. Use the formula from...Ch. S4 - Long-Lived Black Holes. Some scientists speculate...Ch. S4 - Prob. 57EAPCh. S4 - Prob. 58EAPCh. S4 - Prob. 59EAPCh. S4 - Prob. 60EAP
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