Probing the formation of the seeds of supermassive black holes with
  gravitational waves
  The existence of black holes in the intermediate mass interval between one
hundred and ten thousand solar masses, filling the gap between the stellar and
the supermassive black holes is a key prediction to explain the origin of
luminous QSOs at redshifts as large as seven. There is a sheer difficulty in
forming giant black holes of billion suns in less than one billion years. This
has led to the concept of seed black holes. They are high redshift intermediate
mass black holes that formed during cosmic dawn. Seeds are a transient
population, which later grew massive through episodes of accretion and mergers.
In this chapter we explore the possibility of discovering seed black holes and
track their growth across all cosmic epoch, by detecting the gravitational wave
signal they emit at the time of their coalescence, when they pair to form close
binaries. We show that the ESA LISA mission for the detection of low frequency
gravitational waves will be paramount in granting this insight. Gravitational
waves travel unimpeded through the cosmos and carry exquisite information on
the masses and spins of the merging black holes. To this purpose we introduce
key concepts on the gravitational wave emission from binaries, describing
briefly their formation pathway during halo mergers and galaxy collisions.
