Physics 6554: Problem Set 11 Solutions
by Jolyon Bloomeld
April 2013
1
1.1
Question 1
Part a
To show this relation, we work backwards. First, note that
K + w = P P
n .
Then we have the following.
=
P P
=
K + w + n a
(
(
n
+ n n
n
=
n n )( n n ) n +
Physics 6553: Problem Set 10 Solutions 2013
by Jolyon Bloomeld
April 22, 2013
1
Problem 1
We begin by splitting the one-form into components normal and parallel to the surface, v = vb + w .
v
=
(vn
= n
v
+ w )
+v
(1)
n
+
w
(2)
Next, we want to write t
Physics 6553: Problem Set 9 Solutions 2013
by Jolyon Bloomeld and Justin Vines
April 22, 2013
1
Problem 1. Brans-Dicke Gravity
1.1
Part a
Start with the action
S=
where ( )2 = (
a
)(
a ).
w
d4 x g R ( )2 + Sm [g , ]
2
For later convenience, we dene
=
a
a.
Physics 6553: Problem Set 8 Solutions, Spring 2013
by Jolyon Bloomeld and Justin Vines
April 15, 2013
Question 1: Residual Gauge Freedom in Post-Newtonian Gravity
Part a
Here, lets begin by writing out the metric that we start with.
2
gtt = c2 e2/c + O(4)
Physics 6553: Problem Set 7 Solutions, Spring 2013
by Jolyon Bloomeld and Justin Vines
April 15, 2013
Question 1: Stress-energy conservation in Post-Newtonian gravity:
The post-1-Newtonian metric, in conformally Cartesian coordinates, takes the form
ds2 =
Physics 6554: Problem Set 6 Solutions
by Justin Vines and Jolyon Bloomeld
March 2013
1. Asymptotic Energy in Static Spacetimes:
Part a) We start with the metric
ds2 = (xk )2 dt2 + hij (xk )dxi dxj .
We can easily see that
t
=
is a Killing vector, and that
Physics 6554: Problem Set 12 Solutions
by Jolyon Bloomeld
April 2013
1
Question 1
1.1
Part a
AA
Let xAA be the spinor associated with x , using the soldering form by
AA
xAA = x .
Under an SL(2, C) transformation L, the vector in spinor representation tran