  One of the most promising gravitational wave (GW) sources detectable by the
forthcoming LISA observatory are the so-called extreme-mass ratio inspirals
(EMRIs), i.e. GW-driven inspirals of stellar-mass compact objects onto
supermassive black holes (SMBHs). In this paper, we suggest that supernova (SN)
kicks may trigger EMRIs in galactic nuclei by scattering newborn stellar black
holes and neutron stars on extremely eccentric orbits; as a consequence, the
time-scale over which these compact objects are expected to inspiral onto the
central SMBH via GW emission may become shorter than the time-scale for other
orbital perturbations to occur. By applying this argument to the Galactic
Centre, we show that the S-cluster and the clockwise disc are optimal regions
for the generation of such events: one SN out of about 10 000 (100 000)
occurring in the S-cluster (clockwise disc) is expected to induce an EMRI. If
we assume that the natal kicks affecting stellar black holes are significantly
slower than those experienced by neutron stars, we find that most SN-driven
EMRIs involve neutron stars. We further estimate the time spanning from the SN
to the final plunge onto the SMBH to be of the order of few Myr. Finally, we
extrapolate the rate of SN-driven EMRIs per Milky Way to be up to 10^-8/yr,
thus we expect that LISA will detect up to a few tens of SN-driven EMRIs every
year.
