- #1
binbagsss
- 1,259
- 11
Homework Statement
I am trying to follow my lecture notes, attached below, an argument to the number of degrees of freedom from the number of constraints of he Einstein field equations
The bit I a man stuck on is the second thumbnail, and the deduction that he righ hand side of 5.18 only has two derivatives at most. I see that the terms the connection multiplied by G must be a first derivative of the metric multiplied by a second derivative, since ## R \approx \partial\Gamma \implies G \approx \partial^2 g ##
However for the first term I would deduce a third derivative of the metric, since there's another derivative acting on ##G##
So I am unsure how to deduce the right hand side must at most have two derivatives of any type. Do I need to carry out some sort of dimensional analysis ? Obviously these terms must be consistent with each other, in turn consistent with the left hand side? From the second and third term I could agree with the statEment but not the first ? If so, I am unsure how to go about this...
Many thanks
Homework Equations
Above
The Attempt at a Solution
Above[/B]