**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)