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

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.

arXiv comment22 pages, 1 figure

References in corpus (36)

• Tidal Love numbers of neutron stars
• Constraining neutron star tidal Love numbers with gravitational wave detectors
• Relativistic tidal properties of neutron stars
• Isolated and dynamical horizons and their applications
• Relativistic theory of tidal Love numbers
• General Laws of Black-Hole Dynamics
• I-Love-Q Relations in Neutron Stars and their Applications to Astrophysics, Gravitational Waves and Fundamental Physics
• A simple construction of initial data for multiple black holes
• Measurability of the tidal polarizability of neutron stars in late-inspiral gravitational-wave signals
• Dynamical Horizons and their Properties
• Isolated Horizons: Hamiltonian Evolution and the First Law
• Introduction to Isolated Horizons in Numerical Relativity
• Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws
• Generic Isolated Horizons and their Applications
• Local existence of dynamical and trapping horizons
• Geometry of Generic Isolated Horizons
• Mechanics of Isolated Horizons
• Isolated Horizons: A Generalization of Black Hole Mechanics
• Binary-black-hole initial data with nearly-extremal spins
• Multipole Moments of Isolated Horizons
• Introduction to dynamical horizons in numerical relativity
• Nonexistence of conformally flat slices of the Kerr spacetime
• On the gravitational polarizability of black holes
• Geometry and dynamics of a tidally deformed black hole
• Approximate Killing Vectors on S^2
• Spin-Coefficient Form of the New Laws of Black-Hole Dynamics
• Metric of a tidally distorted, nonrotating black hole
• Evolving the Bowen-York initial data for spinning black holes
• Black hole Area-Angular momentum inequality in non-vacuum spacetimes
• Initial data for two Kerr-like black holes
• Angular momentum conservation for dynamical black holes
• Metric-based Hamiltonians, null boundaries, and isolated horizons
• Dynamical Black Holes: Approach to the Final State
• Approximate initial data for binary black holes
• A new method to compute quasi-local spin and other invariants on marginally trapped surfaces
• Perturbative stability of the approximate Killing field eigenvalue problem

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