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I Event and Cauchy horizons for a charged black hole

  1. Jun 8, 2017 #1
    Consider the Reissner-Nordstrom metric for a black hole:

    $$ds^{2} = - f(r)dt^{2} + \frac{dr^{2}}{f(r)} + r^{2}d\Omega_{2}^{2},$$

    where

    $$f(r) = 1-\frac{2M}{r}+\frac{Q^{2}}{r^{2}}.$$

    We can write

    $$f(r) = \frac{1}{r^{2}}(r-r_{+})(r-r_{-}), \qquad r_{\pm} = M \pm \sqrt{M^{2}-Q^{2}}.$$

    Then ##r_{+}## is called the event horizon and ##r_{-}## is called the Cauchy horizon.

    Why is ##r_{+}## called the event horizon and why is ##r_{-}## called the Cauchy horizon?
     
  2. jcsd
  3. Jun 8, 2017 #2

    PeterDonis

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  4. Jun 9, 2017 #3

    Paul Colby

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    Things don't look like they end well for ##|Q| > M##?
     
  5. Jun 9, 2017 #4

    PeterDonis

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    In that case there is no event horizon or Cauchy horizon, just a naked singularity. Most physicists appear to consider that case as not being physically reasonable.
     
  6. Jun 9, 2017 #5
    There are some reasonable examples of naked singularities though: https://arxiv.org/abs/1006.5960
     
  7. Jun 9, 2017 #6

    PeterDonis

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    "Reasonable" does not mean "I have a mathematical model". "Reasonable" means "I have reason to believe this mathematical model describes something that exists in our actual universe". The paper you cite gives no reason to believe that.
     
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