Question

Momentum and pressure have same dimension

Answer 1

Explanation:

To add to the excellent answer already given, in general relativity the right side of the Einstein Field Equations is the “source term”, the stress-energy tensor Tuv (u, v represent Greek letters mu and nu). The lower right 3 X 3 part of the matrix represents the components of momentum flux (T(11) to T(33)) and the diagonal is pressure (the off-diagonals are shear stress). So both have the same units as momentum flux:

Momentum flux = p/Area-time = m*v/Area-time = m*a*t/l^2-t = m*a/l^2 = F/l^2

and force per unit area is of course pressure, or energy density as was mentioned. Likewise, shear stress has the same units, with the velocity vector normal to the projected area instead of parallel as it is for pressure.