# I Event and Cauchy horizons for a charged black hole

1. Jun 8, 2017

### Afonso Campos

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. Jun 8, 2017

3. Jun 9, 2017

### Paul Colby

Things don't look like they end well for $|Q| > M$?

4. Jun 9, 2017

### Staff: Mentor

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.

5. Jun 9, 2017

### Afonso Campos

There are some reasonable examples of naked singularities though: https://arxiv.org/abs/1006.5960

6. Jun 9, 2017

### Staff: Mentor

"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.