I am reading Baez's article http://arxiv.org/pdf/gr-qc/0103044v5.pdf and I do not understand paragraph before equation (10), page 18.(adsbygoogle = window.adsbygoogle || []).push({});

Equation (9) will be true if any one component holds in all local inertial coordinate systems. This is a bit like the observation that all of Maxwell’s equations are contained in Gauss’s law and ∇B= 0. Of course, this is only true if we know how the fields transform under change of coordinates. Here we assume that the transformation laws are known. Given this, Einstein’s equation is equivalent to the fact that ...

1. If any one local component holds in all inertial systems, does this means that we look only ##R_{tt}##, as eq. 10 shows?

2. Why all of Maxwell's equation's are contained in Gauss law and in ##\nabla \bf{B}##? Are both rotor equations unnecessary? Is ##\nabla \bf{B}## not a Gauss law?

3 Is equation 11 mentioned as local inertial systems, not as approximation?

4. Are transformation laws mentioned as pages 88 to 94 in http://arxiv.org/pdf/gr-qc/9712019v1.pdf?

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# Baez's vizualisation of Ricci tensor

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