# Calculating mass from energy momentum tensor

One calculates energy-momentum tensor $T_{\mu\nu}$ from mass. However, is it possible to derive mass from the energy-momentum tensor?

• You can produce an energy-momentum tensor for a particle from its mass density and its 4-velocity, yielding something like $T_{\mu\nu} = m \delta({\bf x}-{\bf x}_0) u_\mu u_\nu$. If the EM-tensor you have have the same overall shape, you can reverse-engineer the mass density, otherwise the best you can is look for the eigenvalue of the time-like eigenvector of the tensor, and call that your proper energy density, which you try to interpret as mass density. – Hydro Guy Feb 5 '18 at 12:19
• @HydroGuy That looks like an answer, not a comment. – sammy gerbil Feb 5 '18 at 15:31
• Ok. Thanks! What do you mean by the time-like eigenvector of the tensor? – physics_2015 Feb 5 '18 at 19:42