Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
9th Edition
ISBN: 9781305932302
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 1, Problem 39P
Review. In a community college parking lot, the number of ordinary cars is larger than the number of sport utility vehicles by 94.7%. The difference between the number of cars and the number of SUVs is 18. Find the number of SUVs in the lot.
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Page 2
SECTION A
Answer ALL questions in Section A
[Expect to use one single-sided A4 page for each Section-A sub question.]
Question A1
SPA6308 (2024)
Consider Minkowski spacetime in Cartesian coordinates th
=
(t, x, y, z), such that
ds² = dt² + dx² + dy² + dz².
(a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V.
(b) Consider now the coordinate system x' (u, v, y, z) such that
u =t-x,
v=t+x.
[2 marks]
Write down the line element, the metric, the Christoffel symbols and the Riemann curvature
tensor in the new coordinates. [See the Appendix of this document.]
[5 marks]
(c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify
explicitly that V. V is invariant under the coordinate transformation.
Question A2
[5 marks]
Suppose that A, is a covector field, and consider the object
Fv=AAμ.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
[5 marks]
(b)…
Chapter 1 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Ch. 1.1 - In a machine shop, two cams are produced, one of...Ch. 1.3 - True or False: Dimensional analysis can give you...Ch. 1.4 - The distance between two cities is 100 mi. What is...Ch. 1 - Prob. 1OQCh. 1 - A house is advertised as having 1 420 square feet...Ch. 1 - Prob. 3OQCh. 1 - Prob. 4OQCh. 1 - Prob. 5OQCh. 1 - Prob. 6OQCh. 1 - Prob. 7OQ
Ch. 1 - Prob. 8OQCh. 1 - Prob. 9OQCh. 1 - Prob. 10OQCh. 1 - Prob. 1CQCh. 1 - Prob. 2CQCh. 1 - Prob. 3CQCh. 1 - Prob. 4CQCh. 1 - Prob. 1PCh. 1 - Prob. 2PCh. 1 - Prob. 3PCh. 1 - Prob. 4PCh. 1 - Prob. 5PCh. 1 - Prob. 6PCh. 1 - A crystalline solid consists of atoms stacked up...Ch. 1 - Prob. 8PCh. 1 - Prob. 9PCh. 1 - Prob. 10PCh. 1 - Prob. 11PCh. 1 - Prob. 12PCh. 1 - The position of a particle moving under uniform...Ch. 1 - (a) Assume the equation x = At3 + Bt describes the...Ch. 1 - A solid piece of lead has a mass of 23.94 g and a...Ch. 1 - Prob. 16PCh. 1 - Prob. 17PCh. 1 - Prob. 18PCh. 1 - Why is the following situation impossible? A...Ch. 1 - Prob. 20PCh. 1 - Prob. 21PCh. 1 - Prob. 22PCh. 1 - Prob. 23PCh. 1 - Prob. 24PCh. 1 - Prob. 25PCh. 1 - Let AI represent the density of aluminum and Fe...Ch. 1 - One gallon of paint (volume = 3.78 103 m3) covers...Ch. 1 - Prob. 28PCh. 1 - Prob. 29PCh. 1 - Prob. 30PCh. 1 - Prob. 31PCh. 1 - (a) Compute the order of magnitude of the mass of...Ch. 1 - To an order of magnitude, how many piano tuners...Ch. 1 - Prob. 34PCh. 1 - Prob. 35PCh. 1 - How many significant figures are in the following...Ch. 1 - The tropical year, the time interval from one...Ch. 1 - Prob. 38PCh. 1 - Review. In a community college parking lot, the...Ch. 1 - Prob. 40PCh. 1 - Prob. 41PCh. 1 - Prob. 42PCh. 1 - Review. The ratio of the number of sparrows...Ch. 1 - Prob. 44PCh. 1 - Prob. 45PCh. 1 - Prob. 46PCh. 1 - Prob. 47PCh. 1 - Prob. 48PCh. 1 - Prob. 49PCh. 1 - Prob. 50PCh. 1 - Prob. 51PCh. 1 - Prob. 52PCh. 1 - Prob. 53PCh. 1 - Prob. 54APCh. 1 - Prob. 55APCh. 1 - Prob. 56APCh. 1 - Prob. 57APCh. 1 - Prob. 58APCh. 1 - Prob. 59APCh. 1 - Prob. 60APCh. 1 - Prob. 61APCh. 1 - The distance from the Sun to the nearest star is...Ch. 1 - Prob. 63APCh. 1 - A spherical shell has an outside radius of 2.60 cm...Ch. 1 - Prob. 65APCh. 1 - Air is blown into a spherical balloon so that,...Ch. 1 - Prob. 67APCh. 1 - In physics, it is important to use mathematical...Ch. 1 - The consumption of natural gas by a company...Ch. 1 - A woman wishing to know the height of a mountain...Ch. 1 - Prob. 71APCh. 1 - Prob. 72APCh. 1 - Prob. 73AP
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