Rotating boson stars and Q-balls

We consider axially symmetric, rotating boson stars. Their flat-space limits represent spinning Q-balls. We discuss their properties and determine their domain of existence. Q-balls and boson stars are stationary solutions and exist only in a limited frequency range. The coupling to gravity gives rise to a spiral-like frequency dependence of the boson stars. We address the flat-space limit and the limit of strong gravitational coupling. For comparison we also determine the properties of spherically symmetric Q-balls and boson stars.