How do you find the killing vectors for Minkowski space?

[fu11meta1]

Homework Statement

How do you find the killing vectors for Minkowski space(or from any metric as well)?

Homework Equations

The Attempt at a Solution

I'm new to GR and I'm going through Carroll's book. I've been alright so far but for some reason I just don't understand what's going on here. Could you guys explain in detail or send me to an online lecture or something to help?

 

[stevendaryl]

If $X^\mu$ is a killing vector field, then it obeys the equation:

$\nabla_\alpha X_\beta + \nabla_\beta X_\alpha = 0$

where $\nabla_\alpha$ is the covariant derivative.

 

[fu11meta1]

I seem to have forgotten notation. -.- I wasn't even thinking of the covariant derivative. Thanks haha