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latentcorpse
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My notes read:
For the gravitational field, we seek an action of the form
[itex]S[g]= \int_M d^4x \sqrt{-g} L[/itex]
where [itex]L[/itex] is a scalar constructed from the metric. An obvious choice for the Lagrangian is [itex]L \propto R[/itex]. This gives the Einstein-Hilbert action
[itex]S_{EH}[g]=\frac{1}{16 \pi} \int_M d^4x \sqrt{-g} R[/itex]
Why is it an obvious choice to pick [itex]L \propto R[/itex]. This is definitely NOT obvious to me!Secondly, if you look at teh notes attached in this thread:
https://www.physicsforums.com/showthread.php?t=457123
On page 107,
where does equation (352) come from? Why is [itex]\Delta^{\mu \nu}=gg^{\mu \nu}[/itex]?
And given eqn (353), how do we get (354)? Did we just det [itex]g \rightarrow -g[/itex]? Where did the [itex]\frac{1}{2}[/itex] come from?
Thanks.
For the gravitational field, we seek an action of the form
[itex]S[g]= \int_M d^4x \sqrt{-g} L[/itex]
where [itex]L[/itex] is a scalar constructed from the metric. An obvious choice for the Lagrangian is [itex]L \propto R[/itex]. This gives the Einstein-Hilbert action
[itex]S_{EH}[g]=\frac{1}{16 \pi} \int_M d^4x \sqrt{-g} R[/itex]
Why is it an obvious choice to pick [itex]L \propto R[/itex]. This is definitely NOT obvious to me!Secondly, if you look at teh notes attached in this thread:
https://www.physicsforums.com/showthread.php?t=457123
On page 107,
where does equation (352) come from? Why is [itex]\Delta^{\mu \nu}=gg^{\mu \nu}[/itex]?
And given eqn (353), how do we get (354)? Did we just det [itex]g \rightarrow -g[/itex]? Where did the [itex]\frac{1}{2}[/itex] come from?
Thanks.
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