We show that the introduction of two worldline parameters defines a different approach to computations in the effective field theory approach to the two-body problem in General Relativity and present some preliminary evidence for a reduction in computational complexity. These parameters obey a polynomial equation whose perturbative expansion recovers an infinite series of diagrams. Futhermore, we show that our equations define an effective two-body horizon for interacting particles in General Relativity; in the circular orbit case, it corresponds to the smallest conceivable separation up to which the orbit can remain circular. We expect our results to simplify higher-order computations in the two-body problem, as well as to give insights on the nonperturbative properties of interacting binaries.
We present a general framework for calculating post-Minskowskian, classical, conservative Hamiltonians for $N$ non-spinning bodies in general relativity from relativistic scattering amplitudes. Novel features for $N>2$ are described including the subtraction of tree-like iteration contributions and the calculation of non-trivial many-body Fourier transform integrals needed to construct position space potentials. A new approach to calculating these integrals as an expansion in the hierarchical limit is described based on the method of regions. As an explicit example, we present the $\mathcal{O}…
We study the Post-Minkowskian (PM) and Post-Newtonian (PN) expansions of the gravitational three-body effective potential. At order 2PM a formal result is given in terms of a differential operator acting on the maximal generalized cut of the one-loop triangle integral. We compute the integral in all kinematic regions and show that the leading terms in the PN expansion are reproduced. We then perform the PN expansion unambiguously at the level of the integrand. Finding agreement with the 2PN three-body potential after integration, we explicitly present new $G^2v^4$-contributions at order 3PN an…
Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
第四后牛顿（4PN）两体动力学最近已经被几种不同的方法处理：有效场论，Arnowitt-Deser-Misner哈密顿量，作用角-Delaunay平均，有效单体，引力自力，动力学第一定律和Fokker作用量。我们回顾这些方法的成就，并讨论其结果的互补性。我们的主要结论是：（i）4PN动力学的第一次完整推导的结果[T.Damour，P.Jaranowski，and G.Schäfer，Phys. Rev. D 89，064058（2014）]已经被几个后续工作分段地完全证实;（ii）德劳内平均技术的结果[T.Damour，P.Jaranowski和G.Schäfer，Phys. Rev. D 91，084024（2015）]已被几项独立工作证实;以及（iii）最近Fokker作用计算中的几个主张[L.Bernard et al.，arXiv：1512.02876v2 [gr-qc]]是不正确的，但可以通过添加与红外和紫外发散正则化中的微妙之处相关的两个模糊参数来校正。
Gravitational waves provide a new probe into the strong-field regime of gravity. It is thus essential to identify the predictions of General Relativity on the nature of the two-body problem, and to contrast them to alternative theories. This thesis aims at comparing the predictions of General Relativity and scalar-tensor theories on gravitational observables using Effective Field Theory techniques. In a first part, we show how simple scalar-tensor theories can be embedded in the Non-Relativistic General Relativity approach to the two-body problem and highlight their essential features. Further…
We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by $n$-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local $SO(n)$ or $SO(n-1,1)$ transformations, `improved diffeomorphisms', and the `generalization of local translations' of the orthonormal frame and the connection. A remarkable aspect of our …
Deformed relativistic kinematics is a framework which captures effects, that are expected from particles and fields propagating on a quantum spacetime, effectively. They are formulated in terms of a modified dispersion relation and a modified momentum conservation equation. In this work we use Finsler geometry to formulate deformed relativistic kinematics in terms of particle velocities. The relation between the Finsler geometric velocity dependent formulation and the original momentum dependent formulation allows us to construct deformed Lorentz transformations between arbitrary frames. Moreo…
One of the open problems in developing binary black hole (BBH) waveforms for gravitational wave astronomy is to model the intermediate mass ratio regime and connect it to the extreme mass ratio regime. A natural approach is to employ the effective one body (EOB) approach to the two-body dynamics that, by design, can cover the entire mass ratio range and naturally incorporates the extreme mass ratio limit. Here we use recently obtained numerical relativity (NR) data with mass ratios $m_1/m_2=(7,15,\,32,\,64,\,128)$ to test the accuracy of the state-of-the-art EOB model TEOBResumS in the interme…
Energy Localization Invariance of Tidal Work in General Relativity
众所周知，当外部广义相对论（电型）潮汐场E（t）与孤立物体的演化四极矩I（t）相互作用时，潮汐场确实对物体做功（"潮汐功"）--即，它将能量传递给物体--以牛顿理论中相同的公式给出的速率：dW/dt =-1/2 E dI/dt。索恩提出了以下问题：鉴于潮汐场和天体之间的引力相互作用能在E（t）I（t）量级上是不明确的，那么潮汐功是否也在这个量级上是不明确的，因此公式dW/dt =-1/2 E dI/dt是否只有在与I（t）的时间尺度相比，在更长的时间尺度上积分时才明确有效？本文完成了一个证明，答案是否定的，dW/dt是不是这样的模棱两可。更具体地说，本文表明，dW/dt是明确地由-1/2 E dI/dt独立的选择如何本地化的引力能在广义相对论。这是证明明确计算dW/dt使用各种引力应力-能量pseudotensors（爱因斯坦，朗道-Lifshitz，穆勒）以及伯格曼的保守量，其中概括了许多pseudotensors，包括一个任意函数的位置。本文还讨论了在广义相对论中建立守恒律的问题以及各种赝张量所起的作用。
We construct a new factorized waveform including $(l,|m|)=(2,2),(2,1),(3,3),(4,4)$ modes based on effective-one-body (EOB) formalism, which is valid for spinning binary black holes (BBH) in general equatorial orbit. When combined with the dynamics of $\texttt{SEOBNRv4}$, the $(l,|m|)=(2,2)$ mode waveform generated by this new waveform can fit the original $\texttt{SEOBNRv4}$ waveform very well in the case of a quasi-circular orbit. We have calibrated our new waveform model to the Simulating eXtreme Spacetimes (SXS) catalog. The comparison is done for BBH with total mass in $(20,200)M_\odot$ us…
Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
