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

Thanks!

(Edit: Make that just the minimally coupled scalar field theory, [tex]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)[/tex] for some positive potential)

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# DEC with E/M and scalar fields

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