# I Killing Vector Of Static Spacetime

1. Apr 3, 2016

### dman12

Hello,

I am reading through some GR lecture notes and have come across the following:

"A spacetime is static if there exists a coordinate chart where:

0gμν = 0
g0i = 0

This spacetime admits a Timelike Killing vector X that satisfies:

XβXγ] = 0 "

How do I go about proving that this relation is true?

Thanks!

David

2. Apr 3, 2016

### Staff: Mentor

Have you tried expanding out the relation that $X$ has to satisfy? Do any terms drop out or cancel because of the properties that the coordinate chart satisfies?