The Effective-One-Body Approach to the General Relativistic Two Body Problem

Damour, Thibault; Nagar, Alessandro

doi:10.1007/978-3-319-19416-5_7

Cited by 75 publications

(45 citation statements)

References 118 publications

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“…test body relative to the background and the total centerof-mass-frame energy of the two-body system, which can be seen to arise from simple special-relativistic kinematics applied to scattering states at infinity. This turned out to be the same as (and gave new insight into) the energy map at the core of effective-one-body (EOB) models for relativistic binary dynamics [33][34][35][36][37][38][39][40][41]. Such EOB models, premised on modeling arbitrary-mass-ratio two-body motion after test-body motion in a fixed background while also incorporating information from PN and selfforce calculations and numerical relativity simulations, have played an important role in the detection and analysis of (including tests of general relativity with) the first gravitational wave signals [1][2][3][4][42][43][44].…”

Section: Introductionmentioning

confidence: 97%

Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings

Vines¹

2018

Class. Quantum Grav.

223

271

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We demonstrate equivalences, under simple mappings, between the dynamics of three distinct systems-(i) an arbitrary-mass-ratio two-spinning-black-hole system, (ii) a spinning test black hole in a background Kerr spacetime, and (iii) geodesic motion in Kerr-when each is considered in the first post-Minkowskian (1PM) approximation to general relativity, i.e. to linear order G but to all orders in 1/c, and to all orders in the black holes' spins, with all orders in the multipole expansions of their linearized gravitational fields. This is accomplished via computations of the net results of weak gravitational scattering encounters between two spinning black holes, namely the net O(G) changes in the holes' momenta and spins as functions of the incoming state. The results are given in remarkably simple closed forms, found by solving effective Mathisson-Papapetrou-Dixon-type equations of motion for a spinning black hole in conjunction with the linearized Einstein equation, with appropriate matching to the Kerr solution. The scattering results fully encode the gaugeinvariant content of a canonical Hamiltonian governing binary-black-hole dynamics at 1PM order, for generic (unbound and bound) orbits and spin orientations. We deduce one such Hamiltonian, which reproduces and resums the 1PM parts of all such previous post-Newtonian results, and which directly manifests the equivalences with the test-body limits via simple effective-one-body mappings.

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Section: Introductionmentioning

confidence: 97%

Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings

Vines¹

2018

Class. Quantum Grav.

223

271

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“…But still, a wave-form model that encompasses mass ratios from comparable to extreme is highly desirable. This is one goal of the effective-one-body (EOB) model [15,14,57,16,24], being probably the best candidate to succeed in this endeavor. While incorporating all O(1) self-force effects is progressing [5], one flavor of EOB models already incorporates the test-spin force on a Kerr background to linear order in the test-spin via a Hamiltonian [10,14], the central piece encoding the conservative dynamics in any EOB model (but see the progress of the other EOB flavor in Refs.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonians and canonical coordinates for spinning particles in curved space-time

Witzany

Steinhoff

Lukes-Gerakopoulos

2019

Class. Quantum Grav.

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The spin-curvature coupling as captured by the so-called Mathisson-Papapetrou-Dixon (MPD) equations is the leading order effect of the finite size of a rapidly rotating compact astrophysical object moving in a curved background. It is also a next-to-leading order effect in the phase of gravitational waves emitted by extreme-mass-ratio inspirals (EMRIs), which are expected to become observable by the LISA space mission. Additionally, exploring the Hamiltonian formalism for spinning bodies is important for the construction of the socalled Effective-One-Body waveform models that should eventually cover all mass ratios.The MPD equations require supplementary conditions determining the frame in which the moments of the body are computed. We review various choices of these supplementary spin conditions and their properties. Then, we give Hamiltonians either in proper-time or coordinate-time parametrization for the Tulczyjew-Dixon, Mathisson-Pirani, and Kyrian-Semerák conditions. Finally, we also give canonical phase-space coordinates parametrizing the spin tensor. We demonstrate the usefulness of the canonical coordinates for symplectic integration by constructing Poincaré surfaces of section for spinning bodies moving in the equatorial plane in Schwarzschild space-time. We observe the motion to be essentially regular for EMRI-ranges of the spin, but for larger values the Poincaré surfaces of section exhibit the typical structure of a weakly chaotic system. A possible future application of the numerical integration method is the inclusion of spin effects in EMRIs at the precision requirements of LISA.

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“…Building libraries of accurate gravitational waveform templates is essential for detecting the coalescence of compact binary systems. To this aim, the effective-one-body (EOB) approach has proven to be a very powerful framework to analytically encompass and combine the post-Newtonian (PN) and numerical descriptions of the inspiral, merger, as well as "ring-down" phases of the dynamics of binary systems of comparable masses in general relativity, see, e.g., [1].…”

Section: Introductionmentioning

confidence: 99%

“…For instance, the corresponding dynamics of binary systems is known at 2.5PN order [2]. 1 What was hence done in [4]- [6] is the computation of ST waveforms at 2PK relative order (although part of this computation requires information on the ST 3PK dynamics, which is, for now, unknown).…”

Section: Introductionmentioning

confidence: 99%

Reducing the two-body problem in scalar-tensor theories to the motion of a test particle: A scalar-tensor effective-one-body approach

Julié

2018

Phys. Rev. D

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Starting from the second post-Keplerian (2PK) Hamiltonian describing the conservative part of the two-body dynamics in massless scalar-tensor (ST) theories, we build an effective-one-body (EOB) Hamiltonian which is a ν-deformation (where ν = 0 is the test mass limit) of the analytically known ST Hamiltonian of a test particle. This ST-EOB Hamiltonian leads to a simple (yet canonically equivalent) formulation of the conservative 2PK two-body problem, but also defines a resummation of the dynamics which is well-suited to ST regimes that depart strongly from general relativity (GR) and which may provide information on the strong-field dynamics, in particular, the ST innermost stable circular orbit (ISCO) location and associated orbital frequency. Results will be compared and contrasted with those deduced from the ST-deformation of the (5PN) GR-EOB Hamiltonian previoulsy obtained in [Phys. Rev. D95, 124054 (2017)].1 or, adopting the terminology of [3], 2.5 post-Keplerian (PK) order, to highlight the fact that (strong) self-gravity effects are encompassed. arXiv:1709.09742v1 [gr-qc] 27 Sep 2017With the same motivation this paper proposes a mapping where the ST-EOB Hamiltonian reduces, in contrast with what was done in paper 1, to the scalar-tensor one-body Hamiltonian in the test mass limit, which describes the motion of a test particle in the metric and scalar field generated by a central SSS body. Although the conservative dynamics derived from this Hamiltonian and that proposed in paper 1 (and from the Mirshekari-Will Lagrangian) are the same at 2PK order, when taken as being exact, they define different resummations and hence, a priori different dynamics in the strong field regime which is reached near the last stable orbit. In particular, we shall highlight the fact that our new, ST-centered, EOB Hamiltonian is well-suited to investigate ST regimes that depart strongly from general relativity.The paper is organised as follows : In section II we present the Hamiltonian describing the motion of a test particle orbiting in the metric and scalar field generated by a central body (when written in Just coordinates) in scalar-tensor theories, henceforth refered as the real one-body Hamiltonian. In order for the paper to be self-contained, in section III we recall the expression of the two-body Hamiltonian in the centre-of-mass frame obtained in paper 1 at 2PK order. In section IV we then reduce the two-body problem to an EOB ν-deformed version of the ST one-body problem, by means of a canonical transformation and imposing the EOB mapping relation between their Hamiltonians. We finally study the resummed dynamics it defines ; in particular, we compute the innermost stable circular orbit (ISCO) location and associated orbital frequency in the case of Jordan-Fierz-Brans-Dicke theory. Corrections to general relativity ISCO predictions are compared to the results obtained in paper 1.

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The Effective-One-Body Approach to the General Relativistic Two Body Problem

Cited by 75 publications

References 118 publications

Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings

Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings

Hamiltonians and canonical coordinates for spinning particles in curved space-time

Reducing the two-body problem in scalar-tensor theories to the motion of a test particle: A scalar-tensor effective-one-body approach

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