5.4 Gravitational Clock Compass
115
04 : R (3)(1)(1)(0) =
3
4
c
−1
33 c
−1
63 (c 33 − c 63 )
−1
(1,1) Bc
2
33 −
(1,1) Bc
2
63
+
(1,3) Bc
2
63 −
(1,6) Bc
2
33
,
(5.95)
05 : R (1)(3)(1)(3) = −3c
−1
33 c
−1
63 (c 33 − c 63 )
−1
(1,1) Bc 33 −
(1,1) Bc 63
+
(1,3) Bc 63 −
(1,6) Bc 33
,
(5.96)
06 : R (1)(2)(1)(3) =
3
2
c
−1
52 c
−1
53
−
(1,5) B + R (1)(0)(1)(0) −
4
3
R (2)(1)(1)(0) c 52
−
4
3
R (3)(1)(1)(0) c 53 −
1
3
R (1)(2)(1)(2) c
2
52 −
1
3
R (1)(3)(1)(3) c
2
53
,
(5.97)
07 : R (2)(0)(2)(0) =
(2,2) B,
(5.98)
08 : R (0)(2)(1)(2) =
3
4
c
−1
11
(2,1) B − R (2)(0)(2)(0) +
1
3
R (1)(2)(1)(2) c
2
11
,
(5.99)
09 : R (3)(2)(2)(0) =
3
4
c
−1
33 c
−1
53 (c 33 − c 53 )
−1
(2,2) Bc
2
33 −
(2,2) Bc
2
53
+
(2,3) Bc
2
53 −
(2,5) Bc
2
33
,
(5.100)
10 : R (2)(3)(2)(3) = −3c
−1
33 c
−1
53 (c 33 − c 53 )
−1
(2,2) Bc 33 −
(2,2) Bc 53
+
(2,3) Bc 53 −
(5,2) Bc 33
,
(5.101)
11 : R (3)(2)(1)(2) =
3
2
c
−1
61 c
−1
63
−
(2,6) B + R (2)(0)(2)(0) +
4
3
R (0)(2)(1)(2) c 61
−
4
3
R (3)(2)(2)(0) c 63 −
1
3
R (1)(2)(1)(2) c
2
61 −
1
3
R (2)(3)(2)(3) c
2
63
,
(5.102)
12 : R (3)(0)(3)(0) =
(3,3) B,
(5.103)