Near-Horizon Metric: Understanding Equation 4.2

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Discussion Overview

The discussion revolves around understanding a specific statement made in an article regarding the behavior of the right-hand side of Equation 4.2 as the horizon is approached in the context of general Kerr-de Sitter metrics. Participants are exploring the implications of this statement and seeking clarification on the underlying reasoning.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about the statement that "as the horizon is approached, the right-hand side of (4.2) approaches zero," and seeks clarification on the reasoning behind it.
  • Another participant suggests looking at Wikipedia for information on the Kerr Solution or Kerr Neumann Metric as a potential resource.
  • A participant acknowledges the generality of the Boyer-Lindquist form and connects the statement to the nature of the horizon as a null hypersurface, but admits uncertainty about the specifics.
  • One participant recommends exploring Killing vector fields, noting that they become null at the event horizon, which may relate to the discussion.
  • A later reply indicates that understanding the near-horizon condition in the context of the rotating reference frame makes the statement about Equation 4.2 more apparent.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are multiple interpretations and suggestions regarding the reasoning behind the statement in Equation 4.2. The discussion remains unresolved with various viewpoints presented.

Contextual Notes

Participants reference different aspects of the Kerr-de Sitter metrics and related concepts, but there are limitations in the clarity of the connections made to the original statement about Equation 4.2. Some assumptions and definitions may not be fully articulated.

vizart
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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.
 
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You might try Wikipedia for a clue,,,
Kerr Solution or Kerr Neumann Metric..
 
Naty1 said:
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 :)
 
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.
 

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