DEC with E/M and scalar fields

1. Nov 2, 2007

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)

Last edited: Nov 2, 2007
2. Nov 2, 2007

Chris Hillman

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

3. Nov 2, 2007

blendecho

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

4. Nov 2, 2007

robphy

So, what did you try in your attempt?

5. Nov 2, 2007

pervect

Staff Emeritus
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)