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

TL;DR

This paper investigates how relativistic effects induce new resonant relations in hierarchical triple systems involving massive black hole binaries and small bodies, significantly affecting the inner orbit's evolution.

Contribution

It introduces a novel relativistic resonance in triple systems with massive black holes, highlighting its stability and impact on orbital dynamics.

Findings

Relativistic effects enable a new stable resonance.

The resonance significantly alters the inner body's orbit.

Relativistic resonances occur even with comparable mass binaries.

Abstract

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