Strong-field tidal distortions of rotating black holes: Formalism and results for circular, equatorial orbits

TL;DR

This paper develops a formalism using black hole perturbation theory to analyze tidal distortions of rapidly rotating black holes in strong gravitational fields, focusing on circular, equatorial orbits and their impact on horizon geometry.

Contribution

It introduces new tools for computing and visualizing tidal distortions of Kerr black holes across all spin parameters in the frequency domain, extending previous Newtonian and fluid body models.

Findings

Distortions depend on black hole spin and orbit parameters.

The horizon's geometry is more complex than in Newtonian models.

Tools for visualizing horizon distortion are developed for spins up to a/M ≤ √3/2.

Abstract

Tidal coupling between members of a compact binary system can have an interesting and important influence on that binary's dynamical inspiral. Tidal coupling also distorts the binary's members, changing them (at lowest order) from spheres to ellipsoids. At least in the limit of fluid bodies and Newtonian gravity, there are simple connections between the geometry of the distorted ellipsoid and the impact of tides on the orbit's evolution. In this paper, we develop tools for investigating tidal distortions of rapidly rotating black holes using techniques that are good for strong-field, fast-motion binary orbits. We use black hole perturbation theory, so our results assume extreme mass ratios. We develop tools to compute the distortion to a black hole's curvature for any spin parameter, and for tidal fields arising from any bound orbit, in the frequency domain. We also develop tools to visualize the horizon's distortion for black hole spin $a/M \le \sqrt{3}/2$ (leaving the more complicated $a/M > \sqrt{3}/2$ case to a future analysis). We then study how a Kerr black hole's event horizon is distorted by a small body in a circular, equatorial orbit. We find that the connection between the geometry of tidal distortion and the orbit's evolution is not as simple as in the Newtonian limit.