Killing tensor notation quick questions

[binbagsss]

My notes read that, the quantity ##K^{2}=K_{uv}V^{u}V^{v}## is constant along geodesics, where ##K## is a killing vector. I know my definition that the quantity on the RHS is conserved, I'm just wondering why do we call it ##K^{2}##, rather than anything else?

In analogy to a killing vector, if ##K## was a killing vector, would we instead call this ##L## or whatver, but without a squared sign?

Thanks in advance for any guidance, or a point towards some notes on this.

 

[binbagsss]

Bump. Also by calling it ##K^{2}## aren't we asumming its positive, how would we know this? thank you.