Is pressure invariant under Lorentz transformations?

Question

In an article from the reference there are following words (page 2): "...pressure P is a Lorentz invariant... the result follows from standart properties of the relativistic stress-energy tensor...".

What properties are used by the authors of an article?

For example, I used the expression for stress-energy tensor of an isotropic body: $$ T_{\alpha \beta} = (\varepsilon + p)\frac{v_{\alpha }v_{\beta}}{c^{2}} - g_{\alpha \beta }p. $$ If pressure is determined as a 3-trace of this tensor, it's obviously that it isn't Lorentz invariant.

Answer 1

I think the pressure here is "defined" by the expression for the stress-energy tensor you wrote down, or equivalently, by $$ p \equiv \frac{1}{3}\left(\frac{v_{\alpha}v_{\beta}}{c^{2}}T^{\alpha\beta}-T^{\alpha}\!{}_{\alpha}\right). $$ My guess is that you probably would have been happier if the author had called this quantity "the pressure in the (locally) comoving frame".