Near-Horizon Metric: Understanding Equation 4.2

[vizart]

I am reading this article http://arxiv.org/abs/hep-th/0404008 on general Kerr-de Sitter metrics.
It seems to be obvious, but I can't see the reason behind the statement that authors make after Equation 4.2 that "As the horizon is approached, the right-hand side of (4.2) approaches zero."
I would be appreciative if somebody could help me with this issue.

 

[Naty1]

You might try Wikipedia for a clue,,,
Kerr Solution or Kerr Neumann Metric..

 

[vizart]

You might try Wikipedia for a clue,,,
Kerr Solution or Kerr Neumann Metric..

thank you for the tip but if you look at the Boyer-Lindquist form #(4.1), you see that it is quite general and i think their statement is somehow related to the fact that the horizon is a null hypersurface. yet i don't know the 'how' part :)

 

[stevebd1]

You might want to take a look at Killing vector fields which become null at the event horizon (i.e. κ=0)

http://en.wikipedia.org/wiki/Killing_vector_field

regards
Steve

 

[vizart]

I must be hanged for not seeing the simple fact that when the metric has the given Lewis form (4.1) if you move to the rotating reference frame, then the near-horizon condition "RHS of Eqn. 4.2 approaches zero" will be obvious.