Tidal deformations of spinning black holes in Bowen-York initial data

TL;DR

This paper analytically investigates how a spinning black hole's horizon shape deforms due to a binary companion, using Bowen-York initial data and quasi-local horizon geometry, focusing on small spins and axisymmetry.

Contribution

It introduces a method to quantify black hole tidal deformations via multipole moments and computes these tidal coefficients analytically in Bowen-York initial data.

Findings

Derived explicit formulas for multipole moments and tidal coefficients.

Quantified the effect of a binary companion on black hole horizon geometry.

Provided analytical results for small-spin, axisymmetric configurations.

Abstract

We study the tidal deformations of the shape of a spinning black hole horizon due to a binary companion in the Bowen-York initial data set. We use the framework of quasi-local horizons and identify a black hole by marginally outer trapped surfaces. The intrinsic horizon geometry is specified by a set of mass and angular-momentum multipole moments $\mathcal{M}_n$ and $\mathcal{J}_n$ respectively. The tidal deformations are described by the change in these multipole moments caused by an external perturbation. This leads us to define two sets of dimensionless numbers, the tidal coefficients for $\mathcal{M}_n$ and $\mathcal{J}_n$, which specify the deformations of a black hole with a binary companion. We compute these tidal coefficients in a specific model problem, namely the Bowen-York initial data set for binary black holes. We restrict ourselves to axisymmetric situations and to small spins. Within this approximation, we analytically compute the conformal factor, the location of the marginally trapped surfaces, and finally the multipole moments and the tidal coefficients.