RGTC-examples

Additional Examples of Calculations with RGTC

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)