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We study the dynamics of merging compact binaries near a rotatingsupermassive black hole (SMBH) in a hierarchical triple configuration. Weinclude various general relativistic effects that couple the inner orbit, theouter orbit and the spin of the SMBH. During the orbital decay due togravitational radiation, the inner binary can encounter an "apsidal precessionresonance" and experience eccentricity excitation. This resonance occurs whenthe apsidal precession rate of the inner binary matches that of the outerbinary, with the precessions driven by both Newtonian interactions and variouspost-Newtonian effects. The eccentricity excitation requires the outer orbit tohave a finite eccentricity, and is most effective for triples with small mutualinclinations, in contrast to the well-studied Lidov-Kozai effect. The resonanceand the associated eccentricity growth may occur while the binary emitsgravitational waves in the low-frequency band, and may be detectable by futurespace-based gravitational wave detectors.

Merging Compact Binaries Near a Rotating Supermassive Black Hole: Eccentricity Excitation due to Apsidal Precession Resonance