# Energy-momentum tensor in the rest frame

Given the energy momentum tensor of a mass in a general frame, how does one derive the energy momentum tensor in the rest frame?

• Are you asking about the energy-momentum $4$-vector $p^{\mu}$? or the stress-energy tensor $T^{\mu \nu}$? – Triatticus May 27 '18 at 3:17
• I meant $T_{\mu\nu}$ – physics_2015 May 27 '18 at 5:27
• There is no guarantee that such a frame exists. Its existence depends on what you mean by "a mass." – Ben Crowell May 27 '18 at 14:25

In the rest frame the momentum vanishes. The momentum density is $T^{i0}$ and the total momentum is the space integral of this. You need to find the Lorentz transformation that makes this quantity vanish.
• OK. Thanks. So, if I understand correctly, one has to transform the energy-momentum tensor to a one which has zero elements except $T_{\mu}0$. If so, how does one Lorentz transform $T_{\mu\nu}$? – physics_2015 May 27 '18 at 9:18
• That is not what I wrote. You need the transformation for which $\int{dV T^{i0}} =0$. – my2cts May 27 '18 at 9:30