  We calculate the gravitational form factors of the pion, sigma meson, and rho
meson in the Nambu-Jona-Lasinio (NJL) model of quantum chromodynamics. The
canonical energy-momentum tensor (EMT) is used in their derivation, allowing
the possibility of an antisymmetric contribution when the hadron has intrinsic
spin. We show that the asymmetric graviton vertex arising from the canonical
EMT satisfies a simpler Ward-Takahashi identity (WTI) than the symmetric
graviton vertex of the Belinfante EMT. The necessity of fully dressing the
graviton vertex through the relevant Bethe-Salpeter equation is demonstrated
for observing both the WTI and a low-energy pion theorem. Lastly, we calculate
static moments of the meson EMT decompositions, obtaining predictions for the
meson mass radii. We find light cone mass radii of 0.27 fm for the pion, 0.32
fm for the sigma, and 0.25 fm for the rho. For the pion and rho, these are
smaller than the light cone charge radii, respectively 0.51 fm and 0.45 fm,
while we have a sigma charge radius of zero. Our light cone pion mass radius
agrees with a phenomenological extraction from KEKB data.
