Stability of rotating relativistic boson stars

We present on progress investigating stability of various rotating relativistic boson stars with non-linear self-interaction potential. It has been shown that there exist relativistic boson stars so compact that they possess bound circular null geodesics, which can have an impact on their stability. Depending on the self-interaction potential, rotating relativistic boson stars exibit a variety of different forms starting from usual donut-like shapes and ending with nearly shell-like structures. Such stars could be interesting alternative candidates for binary star mergers and produce gravitational waveforms that are very different from the waveforms produced in black hole and neutron star mergers.