  We study theoretically phonon-assisted relaxation and inelastic tunneling of
holes in a double quantum dot. We derive hole states and relaxation rates from
kp Hamiltonians and show that there is a finite distance between the dots where
lifetimes of hole states are very long which is related to vanishing tunnel
coupling. We show also that the light hole admixture to hole states can
considerably affect the hole relaxation rates even though its magnitude is very
small.
