The rapid development of gravitational wave instruments will open a completely new
window on the Universe. In this talk, I will describe how this may revolutionize our
understanding of galactic nuclei. Galactic nuclei host a central supermassive black hole,
a dense population of stars and compact objects, and in many cases a bright gaseous
disk feeding the central supermassive black hole. These systems may be a treasure trove
of gravitational wave sources. Recent electromagnetic observations revealed interesting
structures including counterrotating disks and an isotropic central cluster of young stars.
I will demonstrate that these structures can be naturally explained by methods commonly
used in condensed matter physics. Stars and compact objects collectively resemble a gigantic
liquid crystal, which can exhibit phase transitions. Gravitational wave observations may tell us
if there is a central dark cluster or dark disk of compact objects. Ground-based gravitational
wave observatories will be able to constrain the distribution and mass function of black holes.
Pulsar timing can provide a detailed map of this region with unprecedented resolution and locate
intermediate mass black holes, if present.