- #1
Silviu
- 624
- 11
Homework Statement
In an inertial frame O calculate the components of the stress–energy tensors of the following systems:
- (a) A group of particles all moving with the same velocity ##v = \beta e_x##, as seen in O.
Let the rest-mass density of these particles be ##\rho_0##, as measured in their comoving frame. Assume a sufficiently high density of particles to enable treating them as a continuum.
Homework Equations
##T^{\alpha \beta} =\rho_0 U^{\alpha} U^\beta##
The Attempt at a Solution
I used the above equation, and I got the same results as in the book (as the particles can be assumed to be "dust"). However, in the MCRF, the tensor has ##T^{00} = \rho_0## and all the other components equal to 0. If I try to calculate the tensor in another frame moving with speed ##\beta## along the x-axis of this MCRF using ##T^{\alpha ' \beta '} = \Lambda^{\alpha '}_\alpha \Lambda^{\beta '}_\beta T^{\alpha \beta}##. I don't get the same result. Why is this approach wrong? Thank you!