Black Holes are difficult to detect through electromagnetic radiation alone. Indirect evidence for their existence in our universe has been accumulated on a large range of black hole mass scales (supermassive in galactic nuclei, stellar in X-ray binaries and most notably recently by direct gravitational wave detection through LIGO/Virgo). Intermediate mass black holes may exist too, but remain the most speculative variety of their kind. Recently, gravitational waves from coalescing stellar mass black holes have been detected by the LIGO instruments. This is considered a first direct evidence of the existence of black holes and their binaries.
In our team we have been working on the interaction of black holes on all mass scales with stellar clusters surrounding them - globular and nuclear star clusters with stellar mass black holes and galactic nuclei with supermassive ones. We study with computer simulations based on direct N-body simulations with Post-Newtonian general relativity (if needed) how black holes form, build binaries, evolve, disrupt stars, and emit gravitational waves. The talk will give an overview of simulations, methods used and results obtained. Astrophysical topics are for example the ``detection'' of black hole mergers like observed by LIGO in our N-body models; we derive the expected gravitational wave spectrum and waveforms of black hole mergers happening in our computer model and compare it to the observed ones by LIGO. The results give us (with still high uncertainties) clues about the possible origin of observed LIGO events. If time permits we will also discuss how supermassive black hole merges in galactic nuclei, predicted from our models, will show up in future space based low-frequency gravitational wave detectors (such as Euro-American LISA or Chinese Taiji).