  We consider a potentially new class of gravitational wave sources consisting
of a white dwarf coalescing into a massive black hole in the mass range
~10^4-10^5\msun. These sources are of particular interest because the
gravitational wave signal produced during the inspiral phase can be detected by
the Laser Interferometer Space Antenna (LISA) and is promptly followed, in an
extended portion of the black hole and white dwarf mass parameter space, by an
electro-magnetic signal generated by the tidal disruption of the star,
detectable with X-ray, optical and UV telescopes. This class of sources could
therefore yield a considerable number of scientific payoffs, that include
precise cosmography at low redshift, demographics of black holes in the mass
range ~10^4-10^5\Msun, insights into dynamical interactions and populations of
white dwarfs in the cores of dwarf galaxies, as well as a new probe into the
structure and equation of state of white dwarfs. By modelling the gravitational
and electromagnetic radiation produced by these events, we find them detectable
in both observational windows at a distance ~200 Mpc, and possibly beyond for
selected regions of the parameter space. We also estimate the detection rate
for a number of model assumptions about black hole and white dwarf mass
functions and dynamical interactions: the rate is (not surprisingly) highly
uncertain, ranging from ~0.01 yr^-1 to ~100 yr^-1. This is due to the current
limited theoretical understanding and minimal observational constraints for
these objects and processes. However, capture rate scaling arguments favor the
high end of the above range, making likely the detection of several events
during the LISA lifetime.
