# General Relativistic Dynamics of an Extreme Mass-Ratio Binary interacting with an External Body

## TL;DR

This paper investigates the relativistic dynamics of a hierarchical three-body system with an extreme mass ratio, revealing tidal effects, transient resonances, and corrections to the ISCO that could influence gravitational wave signals.

## Contribution

It introduces a novel analysis of tidal effects and transient resonances in relativistic three-body systems, including corrections to the ISCO, relevant for gravitational wave modeling.

## Key findings

- Angular momentum precession due to tidal effects.
- Identification of a transient resonance driven by tidal forces.
- Calculation of tidal correction to the innermost stable circular orbit.

## Abstract

We study the dynamics of a hierarchical three-body system in the general-relativistic regime: an extreme mass-ratio inner binary under the tidal influence of an external body. The inner binary consists of a central Schwarzschild black hole and a compact test body moving around it (outer binary). We discover three types of tidal effects on the orbit of the test body. First, the angular moment of the inner binary precesses around the angular momentum of the outer binary. Second, the tidal field drives a "transient resonance" when the radial and azimuthal frequencies are commensurate with each other. In contrast with resonances driven by the gravitational self-force, this tidal-driven resonance may boost the orbital angular momentum. Finally, as an orbit-dynamical effect during the non-resonant phase, we calculate the correction to the Innermost Stable Circular (mean) Orbit (ISCO) due to the tidal interaction. Hierarchical three-body systems are potential sources for future space-based gravitational wave missions and the tidal effects that we find could contribute significantly to their waveform.