Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field toy model
arXiv:2109.03531 · doi:10.1103/PhysRevD.104.124002
Abstract
The computational cost of inspiral and merger simulations for black-hole binaries increases in inverse proportion to the square of the mass ratio . One factor of comes from the number of orbital cycles, which is proportional to , and another is associated with the required number of time steps per orbit, constrained (via the Courant-Friedrich-Lewy condition) by the need to resolve the two disparate length scales. This problematic scaling makes simulations progressively less tractable at smaller . Here we propose and explore a method for alleviating the scale disparity in simulations with mass ratios in the intermediate astrophysical range (), where purely perturbative methods may not be adequate. A region of radius much larger than around the smaller object is excised from the numerical domain, and replaced with an analytical model approximating a tidally deformed black hole. The analytical model involves certain a priori unknown parameters, associated with unknown bits of physics together with gauge-adjustment terms; these are dynamically determined by matching to the numerical solution outside the excision region. In this paper we develop the basic idea and apply it to a toy model of a scalar charge in a circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field in a 1+1D framework. Our main goal here is to explore the utility and properties of different matching strategies, and to this end we develop two independent implementations, a finite-difference one and a spectral one. We discuss the extension of our method to a full 3D numerical evolution and to gravity.
arXiv comment24 pages, 18 figures
References in corpus (34)
- GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
- GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
- GW190814: Gravitational Waves from the Coalescence of a 23 M Black Hole with a 2.6 M Compact Object
- GW190521: A Binary Black Hole Merger with a Total Mass of
- Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral
- Relativistic tidal properties of neutron stars
- The motion of point particles in curved spacetime
- The SXS Collaboration catalog of binary black hole simulations
- Self-force and radiation reaction in general relativity
- Rapid generation of fully relativistic extreme-mass-ratio-inspiral waveform templates for LISA data analysis
- Second-order self-force calculation of the gravitational binding energy in compact binaries
- Continuum and Discrete Initial-Boundary-Value Problems and Einstein's Field Equations
- Tidal Love Numbers of Kerr Black Holes
- Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency
- Gravitational self-force on generic bound geodesics in Kerr spacetime
- Gravitational-wave energy flux for compact binaries through second order in the mass ratio
- The self-consistent gravitational self-force
- Metrics for next-generation gravitational-wave detectors
- Black hole mergers from dwarf to massive galaxies with the NewHorizon and Horizon-AGN simulations
- Nonrotating black hole in a post-Newtonian tidal environment
- Detectability of Intermediate-Mass Black Holes in Multiband Gravitational Wave Astronomy
- Nonlinear gravitational self-force: second-order equation of motion
- Geometry and dynamics of a tidally deformed black hole
- Understanding initial data for black hole collisions
- Metric of a tidally distorted, nonrotating black hole
- Intermediate mass-ratio black hole binaries: Applicability of small mass-ratio perturbation theory
- Music from the heavens - Gravitational waves from supermassive black hole mergers in the EAGLE simulations
- Optimal Constraint Projection for Hyperbolic Evolution Systems
- A Pseudospectral Method for Gravitational Wave Collapse
- Exploring the small mass ratio binary black hole merger via Zeno's dichotomy approach
- I-Love-Q Relations: From Compact Stars to Black Holes
- Axisymmetric deformations of neutron stars and gravitational-wave astronomy
- Nonrotating black hole in a post-Newtonian tidal environment II
- Adapted gauge to small mass ratio binary black hole evolutions