The metric on [itex]S^2[/itex] is given by,(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\displaystyle ds^2=d\theta^2 + sin^2\theta d\phi^2[/itex]

Here's the answer

[itex] \displaystyle \xi ^{\mu}_{(1)}\partial _{\mu} = \partial_{\phi}[/itex]

[itex] \displaystyle \xi^{\mu}_{(2)}\partial_{\mu} = \ -(cos\phi \partial_{\theta} - cot\theta sin\phi \partial_{\phi}) [/itex]

[itex] \displaystyle \xi^{\mu}_{(3)}\partial_{\mu} = sin\phi \partial_{\theta} + cot\theta cos\phi \partial_{\phi}[/itex]

from Black Hole Physics: Basic Concepts and New Development by Frolov & Novikov

Appendix B

Anyone can explain me how to compute this 3 Killing vector?

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# How we compute killing vector for two-sphere

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