Tidal perturbations of an extreme mass ratio inspiral around a Kerr black hole

TL;DR

This paper develops an analytic framework to understand how external tidal fields deform Kerr black holes and influence the motion of nearby objects, with implications for gravitational wave signals from extreme-mass-ratio inspirals.

Contribution

We analytically reconstruct the metric of a tidally deformed Kerr black hole and derive the secular Hamiltonian for a test particle, revealing spin-dependent tidal effects.

Findings

Tidal corrections significantly depend on black hole spin.

Large tidal effects observed for retrograde orbits around rapidly rotating black holes.

Provides a framework for modeling tidal interactions in gravitational wave sources.

Abstract

We determine the metric of a Kerr black hole subject to external tidal fields using metric reconstruction techniques. Working within the Newman-Penrose formalism, we solve the Teukolsky master equation for static, quadrupolar modes associated with a slowly varying tidal environment, and reconstruct the corresponding metric perturbation in the outgoing radiation gauge. As an application, we derive the secular Hamiltonian governing the motion of a test particle in the tidally deformed Kerr spacetime and investigate long-term tidal effects relevant to extreme-mass-ratio inspirals. In particular, we compute tidal-induced shifts of the innermost stable circular orbit and the light ring. We find that these tidal corrections are strongly spin dependent, with significantly larger effects for retrograde orbits around rapidly rotating black holes. Our results provide a fully analytic framework for studying tidal interactions and secular dynamics in rotating black-hole spacetimes, with direct applications to gravitational-wave modeling and tests of gravity in the strong-field regime.