A Modern Approach to Superradiance

In this paper, we provide a simple and modern discussion of rotational superradiance based on quantum field theory. We work with an effective theory valid at scales much larger than the size of the spinning object responsible for superradiance. Within this framework, the probability of absorption by an object at rest completely determines the superradiant amplification rate when that same object is spinning. We first discuss in detail superradiant scattering of spin 0 particles with orbital angular momentum $\ell=1$, and then extend our analysis to higher values of orbital angular momentum and spin. Along the way, we provide a simple derivation of vacuum friction---a "quantum torque" acting on spinning objects in empty space. Our results apply not only to black holes but to arbitrary spinning objects. We also discuss superradiant instability due to formation of bound states and, as an illustration, we calculate the instability rate $\Gamma$ for bound states with massive spin 1 particles. For a black hole with mass $M$ and angular velocity $\Omega$, we find $\Gamma \sim (G M \mu)^7 \Omega$ when the particle's Compton wavelength $1/\mu$ is much greater than the size $GM$ of the spinning object. This rate is parametrically much larger than the instability rate for spin 0 particles, which scales like $(GM \mu)^9 \Omega$. This enhanced instability rate can be used to constrain the existence of ultralight particles beyond the Standard Model.