The m=2 quadrupole tidal field of a non-spherical nuclear star cluster, with Einstein precession, can drive a supermassive black hole binary to near-unity eccentricity and trigger gravitational-wave circularization within a few billion years.
Therefore, we consid er below only the case α(τ = 0) = 0
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The evolution of a supermassive binary black hole in an non-spherical nuclear star cluster
The m=2 quadrupole tidal field of a non-spherical nuclear star cluster, with Einstein precession, can drive a supermassive black hole binary to near-unity eccentricity and trigger gravitational-wave circularization within a few billion years.