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Killing tensor notation quick questions

  1. Jan 3, 2015 #1
    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.
     
  2. jcsd
  3. Jan 4, 2015 #2
    Bump. Also by calling it ##K^{2}## aren't we asumming its positive, how would we know this? thank you.
     
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