- #1

TerryW

Gold Member

- 169

- 6

## Homework Statement

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.

## Homework Equations

See above

## The Attempt at a Solution

See above