# A Conflicting Faraday Tensor

1. Nov 21, 2017

### Cesarth

Hello, I've found that the Faraday Tensor with both indeces down has in the first line, in MTW Gravitation book (pg 74, eq 3.7), minus the electrical field, while in Wikipedia we find that it is plus the electrical field.
Which one is right?
Does it depend on the signature of the metric?

2. Nov 22, 2017

### robphy

Unfortunately, there are numerous sign conventions in relativity.

The signature sign convention is one: $+---$ , $-+++$ (using the "0" convention for the time coordinate)
...so there is also the ordering of indices: is the time coordinate "0" or "4"?

There is also the definition of the Faraday tensor in terms of how covariant derivatives are notated... $\nabla_{[a} A_{b]}$? $A_{[b;a]}$?
Which index is used to form the electric field? $u^{a}F_{ab}$? $u^{b}F_{ab}$?

In the end, all sources should be describing the same physics... so one might look there to unravel the relationships among the conventions.

3. Nov 22, 2017

### Orodruin

Staff Emeritus
If I do not misremember, there should be a table of different sign conventions and their relative results listed in MTW. I might have confused it with some other book though.