Princip stacionary action for propagation of light is apply on thus definition of action:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]S=\int\!\mbox{d}\tau=\frac{1}{c}\int\!\sqrt{\mbox{d}x_{\mu}\mbox{d}x^{\mu}}=\frac{1}{c}\int\!\sqrt{g_{\mu\nu}\frac{\mbox{d}x^{\nu}}{\mbox{d}\tau}\frac{\mbox{d}x^{\mu}}{\mbox{d}\tau}}\mbox{d}\tau[/tex]

The Evolution coupled Euler-Lagrangian equations we get correct equation of geodetic.

BUT for light-like vectors are true [tex]\mbox{c^2d}\tau^2=\mbox{d}x_{\mu}\mbox{d}x^{\mu}=0[/tex].

Therefore hasn't sense [tex]\frac{\mbox{d}x^{\nu}}{\mbox{d}\tau}[/tex]

and also whole integral for action [tex]S=\int\!\mbox{d}\tau[/tex].

Note: During evolution of E-L equs is dividing of Lagrangian in this case this is dividing of ZERO and this is incorrect.

For time-like or space-like (negativ argument of sqrt is possible neglect or work with comlex number, however E-L equs will still only real) vectors is this operation OK. But variation for light-like vectors isn't (for me) mathematically correct.

Exist another (math. correct) definition of action for light?

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# Is variation pricip for light-geodetic correct?

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