5.4 Gravitational Clock Compass
119
06 : C (0)(3)(1)(3) = −
3
4
c
−1
11
(2,1) B − C (2)(0)(2)(0) −
1
3
C (3)(0)(3)(0) c
2
11
,
(5.121)
07 : C (3)(0)(2)(0) = −
3
2
c
−1
52 c
−1
53
(1,5) B + C (2)(3)(2)(3) +
4
3
C (0)(3)(2)(3) c 52
−
4
3
C (3)(2)(2)(0) c 53 −
1
3
C (3)(0)(3)(0) c
2
52 −
1
3
C (2)(0)(2)(0) c
2
53
,
(5.122)
08 : C (3)(2)(1)(2) = −
3
2
c
−1
61 c
−1
63
(2,6) B − C (2)(0)(2)(0) +
4
3
C (0)(3)(1)(3) c 61
+
4
3
C (3)(2)(2)(0) c 63 −
1
3
C (3)(0)(3)(0) c
2
61 +
1
3
C (2)(3)(2)(3) c
2
63
,
(5.123)
09 : C (3)(1)(3)(2) = −
3
2
c
−1
41 c
−1
42
(3,4) B − C (3)(0)(3)(0) −
4
3
C (0)(3)(1)(3) c 41
−
4
3
C (0)(3)(2)(3) c 42 −
1
3
C (2)(0)(2)(0) c
2
41 +
1
3
C (2)(3)(2)(3) c
2
42
.
(5.124)
With the abbreviations
K 1 :=
3
4
c
−1
33
−
(4,3) B − C (2)(3)(2)(3) + 2C (3)(1)(3)(2) + C (2)(0)(2)(0)
+
1
3
(C (2)(0)(2)(0) − 2C (3)(1)(3)(2) − C (2)(3)(2)(3) )c
2
33
,
(5.125)
K 2 :=
3
4
c
−1
11
−
(5,1) B + C (2)(0)(2)(0) + 2C (3)(0)(2)(0) + C (3)(0)(3)(0)
+
1
3
(C (3)(0)(3)(0) − 2C (3)(0)(2)(0) + C (2)(0)(2)(0) )c
2
11
,
(5.126)
K 3 := −
3
4
c
−1
22
(6,2) B + C (2)(3)(2)(3) − 2C (3)(2)(1)(2) − C (3)(0)(3)(0)
−
1
3
(C (3)(0)(3)(0) − 2C (3)(2)(1)(2) − C (2)(3)(2)(3) )c
2
22
,
(5.127)