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 26, Problem 13OQ
(a)
To determine
Whether the statement is true or false.
(b)
To determine
Whether the statement is true or false.
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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
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[5 marks]
(b)…
Chapter 26 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Ch. 26.1 - A capacitor stores charge Q at a potential...Ch. 26.2 - Many computer keyboard buttons are constructed of...Ch. 26.3 - Two capacitors are identical. They can be...Ch. 26.4 - You have three capacitors and a battery. In which...Ch. 26.5 - If you have ever tried to hang a picture or a...Ch. 26 - Prob. 1OQCh. 26 - Prob. 2OQCh. 26 - Prob. 3OQCh. 26 - Prob. 4OQCh. 26 - Prob. 5OQ
Ch. 26 - Prob. 6OQCh. 26 - Prob. 7OQCh. 26 - Prob. 8OQCh. 26 - Prob. 9OQCh. 26 - Prob. 10OQCh. 26 - Prob. 11OQCh. 26 - Prob. 12OQCh. 26 - Prob. 13OQCh. 26 - Prob. 14OQCh. 26 - Prob. 1CQCh. 26 - Prob. 2CQCh. 26 - Prob. 3CQCh. 26 - Explain why a dielectric increases the maximum...Ch. 26 - Prob. 5CQCh. 26 - Prob. 6CQCh. 26 - Prob. 7CQCh. 26 - Prob. 8CQCh. 26 - (a) When a battery is connected to the plates of a...Ch. 26 - Two conductors having net charges of +10.0 C and...Ch. 26 - Prob. 3PCh. 26 - An air-filled parallel-plate capacitor has plates...Ch. 26 - Prob. 5PCh. 26 - Prob. 6PCh. 26 - When a potential difference of 150 V is applied to...Ch. 26 - Prob. 8PCh. 26 - Prob. 9PCh. 26 - Prob. 10PCh. 26 - Prob. 11PCh. 26 - Review. A small object of mass m carries a charge...Ch. 26 - Prob. 13PCh. 26 - Prob. 14PCh. 26 - Find the equivalent capacitance of a 4.20-F...Ch. 26 - Given a 2.50-F capacitor, a 6.25-F capacitor, and...Ch. 26 - Prob. 17PCh. 26 - Prob. 18PCh. 26 - Prob. 19PCh. 26 - Prob. 20PCh. 26 - A group of identical capacitors is connected first...Ch. 26 - Prob. 22PCh. 26 - Four capacitors are connected as shown in Figure...Ch. 26 - Prob. 24PCh. 26 - Prob. 25PCh. 26 - Prob. 26PCh. 26 - Two capacitors give an equivalent capacitance of...Ch. 26 - Prob. 28PCh. 26 - Prob. 29PCh. 26 - Prob. 30PCh. 26 - Prob. 31PCh. 26 - A 3.00-F capacitor is connected to a 12.0-V...Ch. 26 - Prob. 33PCh. 26 - Prob. 34PCh. 26 - Prob. 35PCh. 26 - Two identical parallel-plate capacitors, each with...Ch. 26 - Two capacitors, C1 = 25.0 F and C2 = 5.00 F, are...Ch. 26 - A parallel-plate capacitor has a charge Q and...Ch. 26 - Prob. 39PCh. 26 - Prob. 40PCh. 26 - Prob. 41PCh. 26 - Prob. 42PCh. 26 - Prob. 43PCh. 26 - Prob. 44PCh. 26 - Determine (a) the capacitance and (b) the maximum...Ch. 26 - Prob. 46PCh. 26 - Prob. 47PCh. 26 - Prob. 48PCh. 26 - Prob. 49PCh. 26 - Prob. 50PCh. 26 - An infinite line of positive charge lies along the...Ch. 26 - Prob. 52PCh. 26 - Prob. 53PCh. 26 - Prob. 54APCh. 26 - Prob. 55APCh. 26 - Prob. 56APCh. 26 - A uniform electric field E = 3 000 V/m exists...Ch. 26 - Prob. 58APCh. 26 - Prob. 59APCh. 26 - Why is the following situation impossible? A...Ch. 26 - Prob. 61APCh. 26 - A parallel-plate capacitor with vacuum between its...Ch. 26 - Prob. 63APCh. 26 - Prob. 64APCh. 26 - Prob. 65APCh. 26 - (a) Two spheres have radii a and b, and their...Ch. 26 - Prob. 67APCh. 26 - A parallel-plate capacitor of plate separation d...Ch. 26 - Prob. 69APCh. 26 - Prob. 70APCh. 26 - To repair a power supply for a stereo amplifier,...Ch. 26 - Prob. 72CPCh. 26 - Prob. 73CPCh. 26 - Consider two long, parallel, and oppositely...Ch. 26 - Prob. 75CPCh. 26 - Prob. 76CPCh. 26 - Prob. 77CPCh. 26 - Prob. 78CP
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