DEC with E/M and scalar fields

[blendecho]

Hi,

I'm trying to show that electromagnetism and scalar field theories satisfy the DEC. I know how to find $$T_{\mu\nu}$$ and all that and what I have to show ($$T_{\mu\nu} T^\nu_{\ \lambda} t^\mu t^\lambda\leq 0$$ and $$T_{\mu\nu} t^\mu t^\nu\geq 0$$ for timelike $$t^\mu$$), but I'm having trouble getting started.

Thanks!

(Edit: Make that just the minimally coupled scalar field theory, $$T_{\mu\nu} = \nabla_\mu \phi \nabla_\nu \phi - \frac{1}{2}g_{\mu\nu}\nabla^\sigma \phi \nabla_\sigma \phi - g_{\mu\nu}V(\phi)$$ for some positive potential)

 

[Chris Hillman]

This is a homework problem, correct? (There is a special PF forum with special rules for these.)

 

[blendecho]

It's a former homework problem, I wasn't satisfied with my solution.

 

[robphy]

So, what did you try in your attempt?

 

[pervect]

This is a homework problem, correct? (There is a special PF forum with special rules for these.)

That applies to undergraduate homework problems. Graduate homework problems can optionally be posted to the main forums. But it is still required to show one's work.

To quote the relevant section from the rules (I should add for people new to the forum that one can click on the link named "rules" to see the current PF rules)

On posting questions: Any and all high school and undergraduate homework assignments or textbook style exercises for which you are seeking assistance are to be posted in the appropriate forum in our Homework & Coursework Questions area.This should be done whether or not the problem is part of one's coursework. The reason for this is that the scientific and mathematical sections of Physics Forums are to be reserved for discussions and not academic assistance. Since graduate level assignments are meant to be more thought provoking (and hence more worthy of discussion), graduate level questions will be allowed in the relevant part of the main section of PF, provided that the graduate student attempts the problem and shows his work.