4-force on a charged particle from the Faraday 2-form in GR

[quasar987]

So apparently (wiki), the manisfestly covariant form of Maxwell's equations is dF=0 and d*F=µJ for F the Faraday 2-form and J the current 3-form. My question will probably seem silly to you but I am simply wondering how does this field affect the motion of a particle of charge q in GR? Is it just $m_0\nabla_{\dot{\gamma}}\dot{\gamma}=f$ for some 4-force vector field f? If so, what is the 4-force f corresponding to a Faraday 2-form F? Thanks again! :)

 

[WannabeNewton]

$u^a\triangledown_au^b = \frac{q}{m}F^{b}{}{}_cu^c$.

 

[tom.stoer]

Have a look at the Einstein-Maxwell-equations

http://en.wikipedia.org/wiki/Maxwell's_equations_in_curved_spacetime

 

[quasar987]

Ok so now I think I understand better what Einstein wanted to do in his later years. He simply wanted to get rid of F=ma altogether! He had done it for gravity and now he wanted to incorporate EM into the geometric structure as well.

 

[WannabeNewton]

quasar you might also be interested in this: http://en.wikipedia.org/wiki/Gravitoelectromagnetism

IMO it is one of the coolest things about GR and there is such a beautiful parallelism between EM and gravity in this context.

 

[quasar987]

That is very cool WBN. Thanks for that link. :)