Saturday, 16 June 2018

homework and exercises - How to show that every Killing vector field is a matter collineation?


Various texts make this claim, but no proof is given.



Explicitly, let L denote the Lie derivative. Suppose LXgab=0 for some vector field X, called a Killing vector field. Suppose that the stress-energy tensor Tab satisfies the Einstein field equations. Then, show that LXTab=0.






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