Black Holes and Charged Particles

[dllahr]

So I guess the equation is wrong?

 

[Ibix]

So I guess the equation is wrong?

I think what Peter is saying is that you are interpreting r as a distance from a centre. It doesn't really have that meaning in black hole spacetimes, since it changes from a space like to a time like coordinate as r varies.

 

[PeterDonis]

I think what Peter is saying is that you are interpreting r as a distance from a centre. It doesn't really have that meaning in black hole spacetimes

Yes, that's what I'm saying.

since it changes from a space like to a time like coordinate as r varies

That's not the real reason, since that property depends on your choice of coordinates. The real reason is that the locus $r = 0$ is not a "point at the center of the black hole". If you look at a Penrose diagram of Reissner-Nordstrom spacetime, you will see that there are actually two timelike lines that both correspond to $r = 0$, and they are both inside the inner horizon. In fact, in the maximally extended geometry, which we have to talk about if we talk about going inside the inner horizon at all, there are an infinite number of such pairs of timelike lines. And, for good measure, these timelike lines are not actually part of the spacetime at all; they are limit points that do not exist in the actual manifold.

 

[PeterDonis]

So I guess the equation is wrong?

The equation is fine; it just doesn't mean what you think it means.

And with that, this thread is closed.