Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy
Donato Bini, Thibault Damour, Andrea Geralico, Stefano Laporta, Pierpaolo Mastrolia
备注：
This paper is a significantly extended version of our previous, separate arxiv submission "Gravitational dynamics at O(G^6): perturbative gravitational scattering meets experimental mathematics" e-Print: 2008.09389 [gr-qc]. The most significant extension is that we now present results at the 7th order in G. 24 pages; revtex macros used; 1 ancillary file
A recently introduced approach to the classical gravitational dynamics of binary systems involves intricate integrals (linked to a combination of nonlocal-in-time interactions with iterated $\frac1r$-potential scattering) which have so far resisted attempts at their analytical evaluation. By using computing techniques developed for the evaluation of multi-loop Feynman integrals (notably Harmonic Polylogarithms and Mellin transform) we show how to analytically compute all the integrals entering the nonlocal-in-time contribution to the classical scattering angle at the sixth post-Newtonian accuracy, and at the seventh order in Newton's constant, $G$ (corresponding to six-loop graphs in the diagrammatic representation of the classical scattering angle).
All-order structure of static gravitational interactions and the seventh post-Newtonian potential
Scuola Normale Superiore（比萨高等师范学院）；INFN Sezione di Pisa（意大利国家核物理研究所比萨分部）；Dipartimento di Fisica e Astronomia, Universita di Padova（帕多瓦大学物理与天文学系）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理学研究所（爱因斯坦研究所））；Institut für Physik und IRIS Adlershof, Humboldt-Universit ät zu Berlin（柏林洪堡大学物理研究所与IRIS阿德勒霍夫中心）；Higgs Centre for Theoretical Physics, University of Edinburgh（爱丁堡大学希格斯理论物理中心）
We calculate the motion of binary mass systems in gravity up to the sixth post--Newtonian order to the $G_N^3$ terms ab initio using momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates. For these contributions we construct a canonical transformation to isotropic and to EOB coordinates at 5PN and agree with the results in the literature \cite{Bern:2019nnu,Damour:2019lcq}. At 6PN we compare to the Hamiltonians in isotropic coordinates either given in \cite{Bern:2019nnu} or resulting from the scattering angle. We find a canonical trans…
We complete our previous derivation, at the sixth post-Newtonian (6PN) accuracy, of the local-in-time dynamics of a gravitationally interacting two-body system by giving two gauge-invariant characterizations of its complementary nonlocal-in-time dynamics. On the one hand, we compute the nonlocal part of the scattering angle for hyberboliclike motions; and, on the other hand, we compute the nonlocal part of the averaged (Delaunay) Hamiltonian for ellipticlike motions. The former is computed as a large-angular-momentum expansion (given here to next-to-next-to-leading order), while the latter is …
Six-loop gravitational interactions at the sixth post-Newtonian order
Scuola Normale Superiore（高等师范学校）；INFN Sezione di Pisa（意大利国家核物理研究所比萨分部）；Universita di Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Humboldt-Universit ät zu Berlin（柏林洪堡大学）；University of Edinburgh（爱丁堡大学）
Binary sources of gravitational waves in the early inspiral phase are accurately described by a post-Newtonian expansion in small velocity and weak interaction. We compute the conservative dynamics to fifth and partial sixth order using a non-relativistic effective field theory. We give predictions for central observables and determine the required coefficients for the construction of an Effective One-Body Hamiltonian, extending the applicability of our results to the late inspiral and merger phases.
Using a recently introduced method [Phys.\ Rev.\ Lett.\ {\bf 123}, 231104 (2019)], which splits the conservative dynamics of gravitationally interacting binary systems into a non-local-in-time part and a local-in-time one, we compute the local part of the dynamics at the sixth post-Newtonian (6PN) accuracy. Our strategy combines several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, effective-field-theory, gravitational self-force, effective one-body, and Delaunay averaging. The full functional structure of the local 6PN Hamiltonian (which involves 151 n…
Using the new methodology introduced in a recent Letter [Phys.\ Rev.\ Lett.\ {\bf 123}, 231104 (2019)], we present the details of the computation of the conservative dynamics of gravitationally interacting binary systems at the fifth post-Newtonian (5PN) level, together with its extension at the fifth-and-a-half post-Newtonian (5.5PN) level. We present also the sixth post-Newtonian (6PN) contribution to the third-post-Minkowskian (3PM) dynamics. Our strategy combines several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, gravitational self-force, effecti…
We consider the Newtonian limit of the theory based on the Lagrangian L = R + \sum a_k R \Box^k R. The gravitational potential of a point mass turns out to be a combination of Newtonian and Yukawa terms. For sixth-order gravity the coefficients are calculated explicitly. For the general case one gets as a result: The the potential is always unbounded near the origin.
We {\it analytically} compute, to the eight-and-a-half post-Newtonian order, and to linear order in the mass ratio, the radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies, thereby extending previous analytic results. These results are obtained by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler's gauge-invariant redshift variable. We emphasize the increase in \lq\lq transcendentality" of the numbers entering the post-Newtonian expansion coefficient…
We determine the gravitational interaction between two compact bodies up to the sixth power in Newton's constant GN, in the static limit. This result is achieved within the effective field theory approach to General Relativity, and exploits a manifest factorization property of static diagrams which allows to derive static post Newtonian (PN) contributions of (2n+1)-order in terms of lower order ones. We recompute in this fashion the 1PN and 3PN static potential, and present the novel 5PN contribution.
A recently introduced approach to the gravitational dynamics of binary systems involves intricate integrals, linked to nonlocal-in-time interactions arising at the 5-loop level of classical gravitational scattering. We complete the analytical evaluation of classical gravitational scattering at the sixth order in Newton's constant, $G$, and at the sixth post-Newtonian accuracy. We use computing techniques developed for the evaluation of multi-loop Feynman integrals to obtain our results in two ways: high-precision arithmetic, yielding reconstructed analytic expressions, and direct integration {…
We introduce a novel framework to study high-order gravitational effects on a binary from the scattering of its emitted gravitational radiation. Here we focus on the radiation-reaction due to the background of the binary's gravitational potential, namely on the so-called tail effects, as the starting point to this type of scattering effects. We start from the effective field theory of a binary composite-particle. Through multi-loop and generalized-unitarity methods, we derive the causal effective actions of the dynamical multipoles, the energy spectra, and the observable flux, due to these eff…
We analyze the coupling between the internal degrees of freedom of neutron stars in a close binary, and the stars' orbital motion. Our analysis is based on the method of matched asymptotic expansions and is valid to all orders in the strength of internal gravity in each star, but is perturbative in the ``tidal expansion parameter'' (stellar radius)/(orbital separation). At first order in the tidal expansion parameter, we show that the internal structure of each star is unaffected by its companion, in agreement with post-1-Newtonian results of Wiseman (gr-qc/9704018). We also show that relativi…
The linear-order effects of radiation-reaction on the classical scattering of two point masses, in General Relativity, are derived by a variation-of-constants method. Explicit expressions for the radiation-reaction contributions to the changes of 4-momentum during scattering are given to linear order in the radiative losses of energy, linear-momentum and angular momentum. The polynomial dependence on the masses of the 4-momentum changes is shown to lead to non-trivial identities relating the various radiative losses. At order $G^3$ our results lead to a streamlined classical derivation of resu…
Analytical calculation of self-force effects on a scalar particle in an eccentric orbit around a Schwarzschild black hole
Scuola Superiore Meridionale（南方高等学院）；INFN, Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Dipartimento di Fisica ”E. Pancini”, Università di Napoli “Federico II”（那不勒斯费德里科二世大学E. Pancini物理系）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理学研究所（爱因斯坦研究所））
Nonlocal-in-time tail effects in gravitational scattering to fifth Post-Minkowskian and tenth self-force orders
II. Institute for Theoretical Physics, Hamburg University（汉堡大学第二理论物理研究所）；Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；School of Physics and Shing-Tung Yau Center, Southeast University（东南大学物理学院暨陈省身数学中心）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）
We perform a Feynman diagram calculation of the two-loop scattering amplitude for gravitationally interacting massive particles in the classical limit. Conveniently, we are able to sidestep the most taxing diagrams by exploiting the test-particle limit in which the system is fully characterized by a particle propagating in a Schwarzschild spacetime. We assume a general choice of graviton field basis and gauge fixing that contains as a subset the well-known deDonder gauge and its various cousins. As a highly nontrivial consistency check, all gauge parameters evaporate from the final answer. Mor…
Using scattering amplitudes, we obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order, ${\cal O}(G^4)$. As in previous lower-order calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves polylogarithms with up to transcendental weight two and elliptic integrals. We derive the radial action directly from the amplitude, and determi…
The Blandford and Znajek (BZ) split-monopole serves as an important theoretical example of the mechanism that can drive the electromagnetic extraction of energy from Kerr black holes. It is constructed as a perturbative low spin solution of Force Free Electrodynamics (FFE). Recently, Armas $et~al.$ put this construction on a firmer footing by clearing up issues with apparent divergent asymptotics. This was accomplished by resolving the behavior around the outer light surface, a critical surface of the FFE equations. Building on this, we revisit the BZ perturbative expansion, and extend the per…
Inspiraling compact binaries with non-negligible orbital eccentricities are plausible gravitational wave (GW) sources for the upcoming network of GW observatories. In this paper, we present two prescriptions to compute post-Newtonian (PN) accurate inspiral templates for such binaries. First, we adapt and extend the post-circular scheme of Yunes {\it et al.} [Phys. Rev. D 80, 084001 (2009)] to obtain a Fourier-domain inspiral approximant that incorporates the effects of PN-accurate orbital eccentricity evolution. This results in a fully analytic frequency-domain inspiral waveform with Newtonian…
We calculate the secular changes of the orbital parameters of a point particle orbiting a Kerr black hole, due to the gravitational radiation reaction. For this purpose, we use the post-Newtonian (PN) approximation in the first order black hole perturbation theory, with the expansion with respect to the orbital eccentricity. In this work, the calculation is done up to the fourth post-Newtonian (4PN) order and to the sixth order of the eccentricity, including the effect of the absorption of gravitational waves by the black hole. We confirm that, in the Kerr case, the effect of the absorption ap…
