The final parsec problem (or last parsec problem) is an astrophysical problem regarding the merger of a binary SMBH, e.g., after a galaxy merger. When the supermassive black holes are extremely close, they merge because gravitational waves significantly bleed their orbital energy. Beyond such extreme closeness, close encounters with stars can remove orbital energy, tightening the orbit, but the odds of encountering a star decreases as the orbit decreases, to a point where the black holes would remain in virtually the same orbit, i.e., the timescale for further decrease is far too long (such as "longer than the age of the universe"). Assuming they sometimes do merge, it is not clear how their orbits continue to become smaller through the final parsec. Thus there is a gap in which neither factor is sufficient to continue to tighten the orbit.
To theorize how the problem might be overcome, obviously both the forces continue to be studied in case there is some reason they are stronger than previously thought. Potential influence of gases, of an accretion disk and/or of a possible third body are also explored.
One possibility is that the distribution of stars in the galaxy core after a merger differs from models developed from/for simpler galaxies, thus allowing dynamical friction to remain significant. Another is the influence of misaligned axes of the black holes and an accretion disk.