What is the most general method of obtaining the event-horizon from the given blackhole metric.(adsbygoogle = window.adsbygoogle || []).push({});

Let us consider Kerr blackhole in Kerr coordinates given by

[tex]

ds^2 = -\frac{\Delta-a^2sin^2\theta}{\Sigma}dv^2+2dvdr -\frac{2asin^2\theta(r^2+a^2-\Delta)}{\Sigma}dvd\chi-2asin^2\theta d\chi dr + \frac{(r^2+a^2)^2-\Delta a^2sin^2\theta}{\Sigma}sin^2\theta d\chi^2+\Sigma d\theta^2,

[/tex]

where

[tex]

\Sigma = r^2+a^2cos^2\theta\\

\Delta = r^2 - 2Mr+a^2.

[/tex]

How do we find the killing vector in a coordinate system?

Any hint or reference would be of great help.

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# Event-horizon from the blackhole metric

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