- #1

- 461

- 0

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

Thanks in advance!

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Philosophaie
- Start date

- #1

- 461

- 0

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

Thanks in advance!

- #2

- 32,761

- 9,863

- #3

WannabeNewton

Science Advisor

- 5,815

- 544

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.

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.

Last edited:

- #4

- 461

- 0

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?

- #5

- 32,761

- 9,863

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

- #6

Bill_K

Science Advisor

- 4,157

- 202

Google "Reissner-Nordstrom derivation" immediately turns up several, including:I have searched the web: Wiki and Bing but I can not find the metric tensor derivations.

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.

Share: