  Spin lattice relaxation rate is investigated for 3D tilted cone Weyl
semimetals (TCWSMs). The nuclear spin relaxation rate is presented as a
function of temperature and tilt parameter. We find that the relaxation rate
behaves as $(1-\zeta^2)^{-\alpha}$ with $\alpha\approx 9$ where $0\le \zeta <
1$ is the tilt parameter. We demonstrate that such a strong enhancement for
$\zeta\lesssim 1$ that gives rise to very fast relaxation rates, is contributed
by the combined effect of a new hyperfine interactions arising from the tilt
itself, and the anisotropy of the ellipsoidal Fermi surface. Extracting an
effective density of states (DOS) $\tilde\rho$ from the Korringa relation, we
show that it is related to the DOS $\rho$ of the tilted cone dispersion by the
"redshift factor" $\tilde\rho=\rho/\sqrt{1-\zeta^2}$. We interpret this
relation as NMR manifestation of an emergent underlying spacetime structure in
TCWSMs.
