The final parsec problem is a traffic jam at the threshold of the strongest gravitational waves in nature. When galaxies merge, their central supermassive black holes sink by dynamical friction and form a bound binary, which hardens by slingshotting stars from the nuclear loss cone. But the loss cone empties: at separations of order a parsec, too few stars remain on intersecting orbits to extract further energy, dynamical friction has long since become inefficient, and gravitational-wave emission will not take over until separations a hundred times smaller (Begelman, Blandford and Rees 1980; Vasiliev 2014). The binary stalls, in principle for longer than a Hubble time.
The stall collides with the evidence for completion. Nuclear star clusters and the scarcity of resolved parsec-scale binaries argue mergers finish; and the nanohertz gravitational-wave background reported by pulsar timing arrays is most naturally read as the chorus of supermassive binaries reaching their final inspirals across cosmic history, requiring coalescence to be routine rather than rare. To bridge stall and chorus, models invoke triaxial galaxy shapes that refill the loss cone, circumbinary gas discs with tuned properties, or successive multi-body black hole encounters (Khan et al. 2013; Merritt 2013), each plausible somewhere, none demonstrably universal, while the bridging must succeed in essentially every merger to feed the background.
The standing is sharpening on the gravitational-wave side: PTA spectral measurements are beginning to constrain the binary population directly, turning the bridge mechanisms from theoretical conveniences into testable requirements.