# Τμ. = Σον δ(x – x (1)) = Σ c2P,"P δ(x – x(t)) = Τυμ, (7.19)...

###### Question:

Τμ. = Σον δ(x – x (1)) = Σ c2P,"P δ(x – x(t)) = Τυμ, (7.19) E. η 1
Question 7.1* (i) The energy-momentum tensor of a perfect fluid, with 4-velocity field UM, is given in an arbitrary frame by (7.24), i.e., TW = (€ + P)U"U"/c - Pg. Contract this expression with gu to evaluate T := T" (ii) Show that in a local inertial frame, in which the fluid is at rest, the above energy momentum tensor simplifies to Twu = diag[pc?, P, P, P]. Use this form to evaluate T directly in this frame. Is the result the same as part (i) above? Why or why not? (iii) For a system of particles comprising photons, use the second summation in (7.19) to show that the corresponding energy-momentum tensor satisfies T=0. Hence, if the system is an perfect fluid (a ‘photon gas”), use part (ii)above to find its equation of state, i.e., to express its energy density in terms of its pressure.

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