- #1

haushofer

Science Advisor

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## Main Question or Discussion Point

Hi there, i have a question about the energy-momentum tensor T of a perfect fluid, en the relations between pressure en density. I've read something about the Dominant Energy condition, which states that the contraction between T and 2 null- or timelike vectors is always positive. This I understand, but it also implies some relations between the pressure and density, and I don't see this. T contains 2 timelike vectors also, can those 2 be identified with the 2 vectors which are used in the contraction, when the T of a perfect fluid is filled in this condition? ( so the normalisation of timelike vectors can be used?)

The book of d'Inverno speaks about turning the question into an eigenvalue problem, in which he turns the eigenvectors in a tetrad. I don't understand this also.....and least but not last, I look for a derivation of the dominant energy condition of Hawking and Ellis ( maybe they use the way which I described earlier? )

If someone could help me, I would be very pleased! I'm busy right now with a little research in cosmology and the cosmological constant, and I'm a little stuck right now :)

The book of d'Inverno speaks about turning the question into an eigenvalue problem, in which he turns the eigenvectors in a tetrad. I don't understand this also.....and least but not last, I look for a derivation of the dominant energy condition of Hawking and Ellis ( maybe they use the way which I described earlier? )

If someone could help me, I would be very pleased! I'm busy right now with a little research in cosmology and the cosmological constant, and I'm a little stuck right now :)