What is the most general method of obtaining the event-horizon from the given blackhole metric.
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.
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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