# What is the “momentum” referred to in the energy-momentum tensor

What is the "momentum" referred to in the energy momentum tensor from GR?

Is it $m\dot{x}$ or is it the canonical momentum $\frac{d}{dt} \left(\frac{\partial L}{\partial \dot{x}}\right)$

Also, I find it very difficult to think of the density and flow of momentum. Momentum is, to me, not an object that moves and has mass, but rather something which characterizes the mass and movement of objects. It is in the same category as things like velocity. So, if someone can explain the intuition behind attributing physical meaning to "momentum density" and "momentum flow," I appreciate it.

• math.ucr.edu/home/baez/gr/stress.energy.html might be of interest – John Rennie Dec 28 '13 at 18:05
• Even in classical mechanics, if an object is not point-like, but occupies some volume $V$ with a mass density $\rho(\vec x)$, and a local speed $\vec v(\vec x)$, the total momentum of the object is the sum of the infinitesimal momenta $\vec p =\int_V d\vec p = \int_V \rho(\vec x) \vec v(\vec x) d^3x$. So $\rho(\vec x) \vec v(\vec x)$ is clearly a momentum density. – Trimok Dec 28 '13 at 18:40