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dwd40physics

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- understanding coordinate transformations of metric and killing vectors

Hi, I am reading through my lecture notes - I haven't formally covered killing vectors but it was introduced briefly in lectures.

Reading through the notes has highlighted something I am not sure about when it comes to co-ordinate transformations.

Q1.Can someone explain how to go from ##\tilde{g}_{uv}## to ##g_{uv} ##

The bit where it says: we can replace the left hand side with ##-\xi^{\lambda}\partial_{\lambda} g_{uv}##

Q2. more basic question how does ##\tilde{g}_{uv}## differ to ##g_{uv} ## ? how does a prime function differ from un-primed functions ?

Q3. what does ##\xi^{\lambda}\partial_{\lambda} g_{uv} = 0 ## tell us ?

thanks :-)

Reading through the notes has highlighted something I am not sure about when it comes to co-ordinate transformations.

Q1.Can someone explain how to go from ##\tilde{g}_{uv}## to ##g_{uv} ##

The bit where it says: we can replace the left hand side with ##-\xi^{\lambda}\partial_{\lambda} g_{uv}##

Q2. more basic question how does ##\tilde{g}_{uv}## differ to ##g_{uv} ## ? how does a prime function differ from un-primed functions ?

Q3. what does ##\xi^{\lambda}\partial_{\lambda} g_{uv} = 0 ## tell us ?

thanks :-)

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