- #1

gnieddu

- 24

- 1

From a mathematical standpoint, I clearly understand what an expression like [tex]v_a = v^bg_{ab}[/tex] means. But let's assume that [tex]v^a[/tex] is, say, a 4-velocity: can I say that [tex]v_a[/tex] is a 4-velocity as well? Or is it something different?

Not to speak of things like [tex]\nabla^av_a[/tex], which can be obtained with some index maths from [tex]\nabla_av^a[/tex]. In my mind, [tex]\nabla_a[/tex] is associated with the idea of covariant derivative, but what about [tex]\nabla^a[/tex]?

Thanks to whoever could shed some light on this.