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Killing vector $\xi_\alpha$ at event horizon of Kerr black hole
I am calculating surface gravity of Kerr Black Hole following 'A Relativist's toolkit' which uses the definition
$$ \left(-\xi^\beta \xi_\beta\right);_\alpha=2\kappa \xi_\alpha$$
where $\kappa$ is ...
- 687
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Surface gravity of a Killing horizon
I have two questions about this:
Surface gravity is defined on the Killing horizon by $\xi^\mu \nabla_\nu \xi^\nu = \kappa \xi^\nu$ for the Killing vector $\xi$. Why can we interpret this as the ...
- 759