Orbits of a Killing vector field

[praharmitra]

I was wondering what the orbits of a Killing vector field are. Do you have any good sources or reading material for this?

 

[bcrowell]

http://www.lightandmatter.com/html_books/genrel/ch07/ch07.html#Section7.1

 

[Sam Gralla]

Given a (not necessarily Killing) vector field V^\mu(x), its "orbits" are solutions Z^\mu(\lambda) to the differential equation \dot{Z}^\mu(\lambda) = V^\mu(Z(\lambda)), where the dot is a \lambda derivative. Intuitively, an orbit just "follows the little arrows of the vector field".

That's all there is to it.

 

[praharmitra]

Given a (not necessarily Killing) vector field V^\mu(x), its "orbits" are solutions Z^\mu(\lambda) to the differential equation \dot{Z}^\mu(\lambda) = V^\mu(Z(\lambda)), where the dot is a \lambda derivative. Intuitively, an orbit just "follows the little arrows of the vector field".

That's all there is to it.

Thanks Sam. I'll do some calculations with this definition and come back if I have further clarifications.

 

[jfy4]

Hall's book on symmetries in GR is my favorite, I'd go so far as to say, I love it.