Binary black hole mergers in star clusters offer rich gravitational wave signatures, such as eccentric events during few-body interactions, precessing binaries, and hierarchical mergers. We developed a rapid code to study all this and much more, relying on Hénon's principle and balanced evolution, Kritos, Strokov, Baibhav, Berti (2024). We can perform thousands of simulations and explore the parameter space of initial conditions without resorting to expensive N-body integration. See also Kritos & Cholis (2021) and Kritos & Cholis (2020) for calculations of merger rates in globular clusters.

What can we learn from observing mergers of binary black holes? Implementing statistical and machine learning methods, we infer the properties of star clusters (such as mass and radius), Ng, Kritos et al. (2023), and binary formation channels, Antonelli, Kritos et al. (2023), based on single merger event characterization. In Kritos, Reali, Antonini, Berti (2024), we explore a scenario where cluster properties can be inferred from detecting the mergers of intermediate-mass black holes with next-generation gravitational wave detectors.

We develop semianalytic models for the growth of stellar-mass black holes in nuclear star clusters through mergers, collisions, and gas accretion, Kritos, Berti, Silk (2022), and Kritos, Berti, Silk (2024). Further growth of these seeds into supermassive black holes is studied by coupling these models with cosmological merger trees from the NewHorizon simulation, Kritos, Beckmann et al. (2024). Measuring the spin of intermediate-mass black holes can also give us an insight into their formation channel, Kritos, Reali, Gerosa, Berti (2024).