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One component of a massive black hole binary (MBHB) might capture a smallthird body, and then a hierarchical, inclined triple system would be formed.With the post-Newtonian approximation including radiation reaction, we analyzedthe evolution of the triple initially with small eccentricities. We found thatan essentially new resonant relation could arise in the triple system. Hererelativistic effects are crucial. Relativistic resonances, including the newone, stably work even for an outer MBHB of comparable masses, and significantlychange the orbit of the inner small body.

Relativistic Resonant Relations between Massive Black Hole Binary and Extreme Mass Ratio Inspiral