2 added 205 characters in body edited Apr 29 at 1:16 Ben Crowell 57.8k66 gold badges172172 silver badges333333 bronze badges 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 $$F^\mu{}_\nu$$. 1 answered Apr 29 at 0:05 Ben Crowell 57.8k66 gold badges172172 silver badges333333 bronze badges 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.