The coalescence of massive black hole binaries is one of the main sources of low‐frequency gravitational radiation that can be detected by LISA. When two galaxies containing massive black holes merge, a binary forms at the center of the new galaxy. We discuss the evolution of the binary after its separation decreases below one parsec. Whether or not stellar dynamical processes can drive the black holes to coalesce depends on the supply of stars that scatter against the binary. We discuss various mechanisms by which this supply can be replenished after the loss cone has been depleted.

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