  We theoretically consider g factor and spin lifetimes of holes in a
longitudinal Ge/Si core/shell nanowire quantum dot that is exposed to external
magnetic and electric fields. For the ground states, we find a large anisotropy
of the g factor which is highly tunable by applying electric fields. This
tunability depends strongly on the direction of the electric field with respect
to the magnetic field. We calculate the single-phonon hole spin relaxation
times T1 for zero and small electric fields and propose an optimal setup in
which very large T1 of the order of tens of milliseconds can be reached.
Increasing the relative shell thickness or the longitudinal confinement length
further prolongs T1. In the absence of electric fields, the dephasing vanishes
and the decoherence time T2 is determined by T2 = 2 T1.
