Self-consistent Effective-one-body theory for spinless binaries based on post-Minkowskian approximation I: Hamiltonian and decoupled equation for ${\psi }_4^B$

Abstract

To build a self-consistent effective-one-body (EOB) theory, in which the Hamiltonian, radiation-reaction force and waveform for the "plus" and "cross" modes of the gravitational wave should be based on the same effective background spacetime, the key step is to look for the decoupled equation for ${\psi }_4^B={\ddot{h}}_{+}-i{\ddot{h}}_{\times }$, which seems a very difficult task because there are non-vanishing tetrad components of the tracefree Ricci tensor for such spacetime. Fortunately, based on an effective spacetime obtained in this paper by using the post-Minkowskian (PM) approximation, we find the decoupled equation for ${\psi }_4^B$ by dividing the perturbation part of the metric into the odd and even parities. With the effective metric and decoupled equation at hand, we set up a frame of self-consistent EOB model for spinless binaries.

16 pages

References in corpus (42)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• Discovery of a Supernova Explosion at Half the Age of the Universe and its Cosmological Implications
• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
• GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• Effective one-body approach to general relativistic two-body dynamics
• Transition from inspiral to plunge in binary black hole coalescences
• Coalescence of Two Spinning Black Holes: An Effective One-Body Approach
• An improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Inspiral, merger and ring-down of equal-mass black-hole binaries
• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Effective-one-body model for black-hole binaries with generic mass ratios and spins
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Toward faithful templates for non-spinning binary black holes using the effective-one-body approach
• Transition from inspiral to plunge in precessing binaries of spinning black holes
• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Inspiral-merger-ringdown multipolar waveforms of nonspinning black-hole binaries using the effective-one-body formalism
• Prototype effective-one-body model for nonprecessing spinning inspiral-merger-ringdown waveforms
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-spinning, equal-mass black holes
• An improved analytical description of inspiralling and coalescing black-hole binaries
• Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
• Fourth post-Newtonian effective one-body dynamics
• A waveform model for eccentric binary black hole based on effective-one-body-numerical-relativity (EOBNR) formalism
• Comparing Effective-One-Body gravitational waveforms to accurate numerical data
• A data-analysis driven comparison of analytic and numerical coalescing binary waveforms: nonspinning case
• Using Full Information When Computing Modes of Post-Newtonian Waveforms From Inspiralling Compact Binaries in Circular Orbit
• Accurate Effective-One-Body waveforms of inspiralling and coalescing black-hole binaries
• High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-precessing, spinning, equal-mass black holes
• Faithful Effective-One-Body waveforms of equal-mass coalescing black-hole binaries
• Gravitational spin-orbit coupling in binary systems at the second post-Minkowskian approximation
• Modeling multipolar gravitational-wave emission from small mass-ratio mergers
• Post-Newtonian expansion of gravitational waves from a particle in circular orbit around a Schwarzschild black hole
• Gauge Invariant Perturbations of the Schwarzschild Spacetime

Cited by in corpus (12)

• QNMs of slowly rotating Einstein-Bumblebee Black Hole
• Gauge Invariant Perturbations of General Spherically Symmetric Spacetimes
• New self-consistent effective one-body theory for spinless binaries based on the post-Minkowskian approximation
• Self-consistent effective-one-body theory for spinning binaries based on post-Minkowskian approximation
• Entanglement dynamics in $\kappa$-deformed spacetime
• Dissipation suppression for an Unruh-DeWitt battery with a reflecting boundary
• Determination of the spin parameter and the inclination angle by the relativistic images in black hole image
• The ring-shaped shadow of rotating naked singularity with a complete photon sphere
• Strong gravitational lensing of rotating regular black holes in non-minimally coupled Einstein-Yang-Mills theory
• Effective metric of spinless binaries with radiation-reaction effect up to fourth Post-Minkowskian order in effective-one-body theory
• Gravitational wave fluxes on generic orbits in near-extreme Kerr spacetime: higher spin and large eccentricity
• Energy flux and waveform of gravitational wave generated by coalescing slow-spinning binary system in effective one-body theory