(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Occasional, MTW's use of language is a bit obscure. I've highlighted a section from p491 (attached) which I just can't make any sense of.

I know about the 20 components of R_{αβγδ}but what does "these twenty components are arbitrary to the extent of the six parameters of a local Lorentz transformation" actually mean? And are they actually referring to R_{αβγδ}, because it goes on to say "However,^{(4)}R is the only one of these 14 quantities...." which seems to imply that we aren't talking about the 20 R_{αβγδ}. So what are the 20 components? And what are the 6 parameters of the local Lorentz transformation?

Also, in the context of a local Lorentz transformation, where g_{αβ,γ}= 0, all the values of R_{αβγδ}are linear in the second derivatives because R_{αβγδ}= Γ_{αβδ,γ}- Γ_{αβγ,δ}because the ΓΓ terms are all zero.

2. Relevant equations

See above

3. The attempt at a solution

See above

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# Homework Help: MTW Chapter 21 Arcane Language

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