Hy aatw! Welcome to PF!Hy.
Can somebody please show me the way, how to transform stress-energy tensor for sphere in rest frame to stress-energy tensor in rotating frame using Lorentz transformations?
No, if [itex]g = \eta[/itex] then [itex]T^{ij} = P \delta^i_j[/itex] where P is the pressure between the elements (just use the formula you quoted with [itex]u^a = (1,0,0,0)[/itex] -which is the 4-velocity in the rest frame).Thanks for your quick reply.
Maybe I didn't express myself so well.
Let's start from stress-energy tensor for sphere, which can be written as [tex]T^{ab} = (\rho + p) u^a u^b + p g^{ab}[/tex], but in rest frame where sphere doesn't rotate, it's only [tex]T^{00}[/tex] element that's nonzero (I think so!).
ok, so just use an ordinary boost in all 3 spacial directions with [itex]v=\omega r[/itex]But now sphere starts to rotate with angular speed [tex]\omega[/tex] around z axis and I want to use Lorentz transformation to determine [tex]T^{ab}[/tex] for rotating sphere.