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Misner, Thorne, and Wheeler have a nice two-page summary of sign conventions in general relativity, in the front endpapers of the book, so that would be the first place I would turn for this kind of thing.

The electromagnetic tensor is defined by the Lorentz force equation, which gives the four-force acting on a charged particle as $f^a=qF^a{}_bv^b$. The definition of the upper-index four-force and four-velocity have nothing to do with the choice of signature, so the formcomponents of the mixed-index electromagnetic tensor does$F^\mu{}_\nu$ do not depend on the choice of signature. The forms $F_{\mu\nu}$ and $F^{\mu\nu}$ do have components that depend on the signature, and they can be found, if required, from the components of $F^\mu{}_\nu$.

Misner, Thorne, and Wheeler have a nice two-page summary of sign conventions in general relativity, in the front endpapers of the book, so that would be the first place I would turn for this kind of thing.

The electromagnetic tensor is defined by the Lorentz force equation, which gives the four-force acting on a charged particle as $f^a=qF^a{}_bv^b$. The definition of the four-force and four-velocity have nothing to do with the choice of signature, so the form of the electromagnetic tensor does not depend on the choice of signature.

Misner, Thorne, and Wheeler have a nice two-page summary of sign conventions in general relativity, in the front endpapers of the book, so that would be the first place I would turn for this kind of thing.

The electromagnetic tensor is defined by the Lorentz force equation, which gives the four-force acting on a charged particle as $f^a=qF^a{}_bv^b$. The definition of the upper-index four-force and four-velocity have nothing to do with the choice of signature, so the components of the mixed-index electromagnetic tensor $F^\mu{}_\nu$ do not depend on the choice of signature. The forms $F_{\mu\nu}$ and $F^{\mu\nu}$ do have components that depend on the signature, and they can be found, if required, from the components of $F^\mu{}_\nu$.

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source | link

Misner, Thorne, and Wheeler have a nice two-page summary of sign conventions in general relativity, in the front endpapers of the book, so that would be the first place I would turn for this kind of thing.

The electromagnetic tensor is defined by the Lorentz force equation, which gives the four-force acting on a charged particle as $f^a=qF^a{}_bv^b$. The definition of the four-force and four-velocity have nothing to do with the choice of signature, so the form of the electromagnetic tensor does not depend on the choice of signature.