Metric Tensor of the Reissner–Nordström Metric

[Philosophaie]

I am looking for the Metric Tensor of the Reissner–Nordström Metric.$$g_{μv}$$
I have searched the web: Wiki and Bing but I can not find the metric tensor derivations.

Thanks in advance!

 

[Dale]

http://en.wikipedia.org/wiki/Reissner–Nordström_metric

 

[WannabeNewton]

As far as deriving it goes, you can do this easily yourself if you've seen the standard derivation of the Schwarzschild solution before. The only extra thing you would have to do is solve the source-free Maxwell equations $\nabla_{[\gamma}F_{\mu\nu]} = 0$ and $\nabla^{\mu} F_{\mu\nu} = 0$ simultaneously with the electrovacuum field equations $G_{\mu\nu} = 8\pi T^{EM}_{\mu\nu}$ but because we are dealing with a spherically symmetric static source, you can easily deduce $F_{\mu\nu}$ by working in the coordinates adapted to all the symmetries of the space-time and then solve $G_{\mu\nu} = 8\pi T^{EM}_{\mu\nu}$ in said coordinates.

Alternatively, you can derive the solution without using coordinates at all; you would be doing all of your calculations (right before you write down the actual solution) in a coordinate-free manner. This is harder but in my opinion much more insightful than just going through the mindless coordinate computations.

 

[Philosophaie]

As far as deriving it goes, you can do this easily yourself if you've seen the standard derivation of the Schwarzschild solution before.

Alternatively, you can derive the solution without using coordinates at all; you would be doing all of your calculations (right before you write down the actual solution) in a coordinate-free manner. This is harder but in my opinion much more insightful than just going through the mindless coordinate computations.

I have never seen the Reissner–Nordström Metric Tensor derived before from its metric. The Schwarzschild Metric Tensor is difficult enough.

Is there any websites that go thru the and simplifies the derivation of either of these Non-rotating Charged or Uncharged Metric Tensor Components from its Metric?

 

[Dale]

Oops, sorry. I didn't notice that you wanted a derivation, not just the metric itself.

 

[Bill_K]

I have searched the web: Wiki and Bing but I can not find the metric tensor derivations.

Google "Reissner-Nordstrom derivation" immediately turns up several, including:

http://gmammado.mysite.syr.edu/notes/RN_Metric.pdf
http://arxiv.org/pdf/physics/0702014.pdf

Actually the easiest way to obtain the Reissner-Nordstrom metric is not to start from scratch, but to derive it from Schwarzschild using the Harrison transformation.