1 Choosing simpRules (answers to exercises in RGTC.nb)
(a) Schwarzschild's solution in Kruskal coordinates (see Section 4.3): Kruskal (16 KB)
(b) Verifying Bianchi[1] for Example 5:
Example5Bianchi (45 KB)
2 Constructing new tensors
Bach and Bell-Robinson Tensors (50 KB)
3 Using series expansions
(a) General 1st order perturbation of the Schwarzschild metric: unevaluated (12 KB), evaluated (185 KB)
(b) Asymptotic form of the Bondi metric near infinity in an NP null frame:
unevaluated (51 KB),
evaluated (240 KB)
4 Verification of the Tomimatsu - Sato solutions for n = 1, 2, 3
(a) Direct computation: TS123.nb (12 KB), TS123EV.nb (500 KB)
(b) Alternate approaches:
TS123Alt.nb (24 KB),
TS123AltEV.nb
(730 KB)
5 Incomplete simplifications may lead to wrong conclusions (see RGTC.nb, section 4.6 (iii))
(a) Properties of n-dimensional sphere metrics: nDimSpheres.nb (70 KB)
(b) Failure to recognize deList closure:
EliminateTrigFunctions.nb (20 KB)
6 Testing the correctness of RGTC results: Independent calculations of the same quantities
Quadratic, cubic and differential invariants of the Kerr metric:
KerrInvariants.nb (140 KB)
7 Classify on approximate metrics can lead to misleading results
Classifying a perturbed Schwarzschild metric at different orders of approximation:
ClassifyApproximateMetrics.nb (220 KB)