Lie Derivative in Relativity: Examples & Uses

[kent davidge]

Can someone point me some examples of how the Lie Derivative can be useful in the General theory of Relativity, and if it has some use in Special Relativity.

I'm asking this because I'm studying how it's derived and I don't have any Relativity book in hand so that I can look up its application (and I'm not even sure whether it's easy to find out).

 

[haushofer]

Diffeomorphisms are generates by lie derivatives. So e.g. to find isometries one puts the lie derivative of the metric to zero and solves for the vector field, giving so called Killing vectors.

 

[haushofer]

See e.g. Carroll's GR notes .