qnm

QNM, or quasi-normal mode, is a damped oscillation that characterizes how a perturbed system returns to equilibrium when energy is radiated away, typically by gravitational waves or other fields. In general relativity, black holes and compact stars admit a discrete set of QNMs. Each mode has a complex frequency ω = ωR − iωI, where ωR is the oscillation frequency and ωI the damping rate. The imaginary part implies exponential decay with timescale τ = 1/ωI. The spectrum depends primarily on the macroscopic parameters of the object, such as the mass and spin (and charge in the charged Kerr-Newman case).

QNMs are defined by specific boundary conditions: waves ingoing at the event horizon and outgoing at infinity for asymptotically flat spacetimes. They are intrinsic to the spacetime geometry and do not depend on the details of the perturbation, making them universal fingerprints of the remnant object.

In astrophysics, the ringdown phase of a black hole merger is well described by a superposition of QNMs. Measuring QNM frequencies from gravitational-wave data allows inference of the remnant's mass and spin and provides a test of general relativity, including the no-hair theorem. Beyond astrophysics, QNMs also appear in anti-de Sitter spacetimes and in other wave systems.

Some sources use "qnm" as shorthand for quasi-normal mode; in practice the term is widely used in physics literature and related software to denote these modes.