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Im interested in surface gravity of Kerr black hole it means, I need to find killing vector for Kerr which is null on outer horizont. Is it true? How should I do that? I guess it could be some linear combination of vecotrs ∂/∂t and ∂/∂[itex]\phi[/itex]. So can I looking for that this way?[itex][/itex]

[itex]\chi=(a,0,0,b)[/itex] and than from limit [itex]g_{\mu\nu}\chi^{\mu}\chi^{\nu}=0[/itex], [itex]r→r_{+}[/itex], where [itex]r_{+}[/itex] is outer horizon?

I find out [itex]b=a\frac{-g_{\phi t}\pm \sqrt{g_{\phi t}^2-g_{tt}g_{\phi \phi}}}{g_{\phi \phi}}[/itex] for [itex]r→r_{+}[/itex].

Is it right? What is it telling me?

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# Surface gravity (Killing vecotrs) of Kerr black hole

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