Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 30, Problem 26P
(a)
To determine
The unknown nuclide in the equation
(b)
To determine
The unknown nuclide in the equation
(c)
To determine
The unknown nuclide in the equation
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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 30 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 30.1 - Prob. 30.1QQCh. 30.1 - Prob. 30.2QQCh. 30.3 - Prob. 30.3QQCh. 30.3 - Suppose you have a pure radioactive material with...Ch. 30.4 - Which of the following is the correct daughter...Ch. 30.4 - Which of the following is the correct daughter...Ch. 30 - Prob. 1OQCh. 30 - Prob. 2OQCh. 30 - Prob. 3OQCh. 30 - Prob. 4OQ
Ch. 30 - Prob. 5OQCh. 30 - Prob. 6OQCh. 30 - Prob. 7OQCh. 30 - Prob. 8OQCh. 30 - Prob. 9OQCh. 30 - Prob. 10OQCh. 30 - Which of the following quantities represents the...Ch. 30 - Prob. 12OQCh. 30 - Prob. 1CQCh. 30 - Prob. 2CQCh. 30 - Prob. 3CQCh. 30 - Prob. 4CQCh. 30 - Prob. 5CQCh. 30 - Prob. 6CQCh. 30 - Prob. 7CQCh. 30 - If no more people were to be born, the law of...Ch. 30 - Prob. 9CQCh. 30 - Prob. 10CQCh. 30 - Prob. 11CQCh. 30 - What fraction of a radioactive sample has decayed...Ch. 30 - Prob. 13CQCh. 30 - Prob. 14CQCh. 30 - Prob. 15CQCh. 30 - Prob. 16CQCh. 30 - Prob. 17CQCh. 30 - Prob. 1PCh. 30 - Prob. 2PCh. 30 - Prob. 3PCh. 30 - Prob. 4PCh. 30 - Prob. 5PCh. 30 - Prob. 6PCh. 30 - Prob. 7PCh. 30 - Prob. 8PCh. 30 - Prob. 9PCh. 30 - Prob. 10PCh. 30 - Prob. 11PCh. 30 - Prob. 12PCh. 30 - Prob. 13PCh. 30 - Prob. 14PCh. 30 - Prob. 16PCh. 30 - Prob. 17PCh. 30 - Prob. 18PCh. 30 - What time interval elapses while 90.0% of the...Ch. 30 - Prob. 20PCh. 30 - Prob. 21PCh. 30 - Prob. 22PCh. 30 - Prob. 23PCh. 30 - Prob. 24PCh. 30 - Prob. 25PCh. 30 - Prob. 26PCh. 30 - Prob. 27PCh. 30 - Prob. 28PCh. 30 - Prob. 29PCh. 30 - Prob. 30PCh. 30 - Prob. 31PCh. 30 - Prob. 32PCh. 30 - Prob. 33PCh. 30 - Prob. 34PCh. 30 - Prob. 35PCh. 30 - Prob. 36PCh. 30 - Prob. 37PCh. 30 - Prob. 38PCh. 30 - Prob. 39PCh. 30 - Prob. 41PCh. 30 - Prob. 42PCh. 30 - Prob. 43PCh. 30 - Prob. 45PCh. 30 - Prob. 46PCh. 30 - Prob. 47PCh. 30 - Prob. 48PCh. 30 - Prob. 49PCh. 30 - Prob. 50PCh. 30 - Prob. 51PCh. 30 - Prob. 52PCh. 30 - Prob. 53PCh. 30 - Prob. 54PCh. 30 - Prob. 55PCh. 30 - Prob. 56PCh. 30 - Prob. 57PCh. 30 - Prob. 58PCh. 30 - Prob. 59PCh. 30 - Prob. 60PCh. 30 - Prob. 61PCh. 30 - Prob. 62PCh. 30 - Prob. 63PCh. 30 - Prob. 64PCh. 30 - Prob. 65PCh. 30 - Prob. 66PCh. 30 - Prob. 67PCh. 30 - Prob. 68PCh. 30 - Prob. 69PCh. 30 - Prob. 70P
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