Superradiance -- the 2020 Edition

TL;DR

The work surveys superradiance as a universal energy-extraction mechanism that requires dissipation and the presence of an ergoregion, unifying flat-space phenomena (Klein paradox, Cherenkov-like effects, and sonic analogs) with curved-spacetime physics around black holes. It develops a comprehensive framework for SR in black-hole spacetimes, detailing master equations, amplification factors across spins, backreaction effects, and non-linear evolutions, including BH bombs and hairy BHs in AdS and beyond-GR theories. The review emphasizes the astrophysical and laboratory implications, including constraints on ultralight bosons, holographic interpretations, and analogue gravity experiments, while outlining open issues and directions in higher dimensions, non-asymptotically flat spacetimes, and scalar-tensor frameworks. Overall, the article provides a cohesive, multi-domain picture of SR, its instabilities, end-states, and potential observational signatures. It highlights how confinement—via mirrors, AdS boundaries, or effective masses—drives instabilities and shapes the landscape of possible compact-object configurations, with wide-ranging consequences from fundamental physics to astrophysical phenomenology.

Abstract

Superradiance is a radiation enhancement process that involves dissipative systems. With a 60 year-old history, superradiance has played a prominent role in optics, quantum mechanics and especially in relativity and astrophysics. In General Relativity, black-hole superradiance is permitted by the ergoregion, that allows for energy, charge and angular momentum extraction from the vacuum, even at the classical level. Stability of the spacetime is enforced by the event horizon, where negative energy-states are dumped. Black-hole superradiance is intimately connected to the black-hole area theorem, Penrose process, tidal forces, and even Hawking radiation, which can be interpreted as a quantum version of black-hole superradiance. Various mechanisms (as diverse as massive fields, magnetic fields, anti-de Sitter boundaries, nonlinear interactions, etc...) can confine the amplified radiation and give rise to strong instabilities. These "black-hole bombs" have applications in searches of dark matter and of physics beyond the Standard Model, are associated to the threshold of formation of new black hole solutions that evade the no-hair theorems, can be studied in the laboratory by devising analog models of gravity, and might even provide a holographic description of spontaneous symmetry breaking and superfluidity through the gauge-gravity duality. This work is meant to provide a unified picture of this multifaceted subject. We focus on the recent developments in the field, and work out a number of novel examples and applications, ranging from fundamental physics to astrophysics.

Figures (75)

• Figure 1: Amplification values $Z_{0m}=|{\cal R}|^2/|{\cal I}|^2-1$ of the scalar toy model for $m=1$, $\Omega R=0.5$ and $\alpha R=0.1,2$.
• Figure 2: Left panel: Amplification values $Z_{m}$ of acoustic waves for $m=1,\,R=10\,{\rm cm}$ and $\Omega=1000,\,2000\,{\rm s}^{-1}$. Right panel: fundamental unstable mode for the "acoustic bomb", a rotating cylinder with radius $R$ enclosed in a cylindrical cavity at distance $R_2$. In this example we set $m=1$ and $v/c_s\approx 0.147$. Note that the mode becomes unstable $(\omega_I>0)$ precisely when the superradiance condition $\omega_R<\Omega$ is fulfilled.
• Figure 3: Tides on the Earth caused by our moon (as seen by a frame anchored on the Moon). The tidal forces create a bulge on Earth's ocean surface, which leads Moon's orbital position by a constant angle $\phi$. Earth rotates faster than the Moon in its orbit, thus a point $A$ on the surface of the Earth will differentially rotate with respect to the oceans, causing dissipation of energy and decrease of Earth's rotation period.
• Figure 4: Frame dragging effects: sketch of the trajectory of a zero-angular-momentum observer as it falls into a BH. The BH is either static (upper panel) or rotating clockwise (lower panel). The infall into a rotating BH is drag along the BH's sense of rotation.
• Figure 5: The ergosphere of a Kerr BH is shown together with the horizon for a nearly-extremal BH with $a\sim 0.999M$. The coordinates $(x,y,z)$ are similar to standard Cartesian-coordinate but obtained from the Boyer-Lindquist coordinates.