Killing tensor notation quick questions

  • Thread starter binbagsss
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  • #1
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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.
 

Answers and Replies

  • #2
1,232
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Bump. Also by calling it ##K^{2}## aren't we asumming its positive, how would we know this? thank you.
 

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