Third post-Newtonian effective-one-body Hamiltonian in scalar-tensor and Einstein-scalar-Gauss-Bonnet gravity
Third post-Newtonian effective-one-body Hamiltonian in scalar-tensor and Einstein-scalar-Gauss-Bonnet gravity
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DOI：
10.1103/physrevd.107.104044
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发表时间：
2022-12
影响因子：
5
通讯作者：
F'elix-Louis Juli'e;V. Baibhav;E. Berti;A. Buonanno
中科院分区：
文献类型：
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作者：
F'elix-Louis Juli'e;V. Baibhav;E. Berti;A. Buonanno
在标量张量引力理论和Einstein-scalar-Gauss-Bonnet引力理论中建立了一个三阶后牛顿（3 PN）有效单体（EOB）哈密顿量。后者是广义相对论的延伸，它预言了黑洞的标量头发。我们从已知的3 PN阶二体拉格朗日量出发，利用降阶方法构造了它的普通哈密顿量。然后，我们减少保守的两体动力学的（nongeodesic）运动的测试粒子在一个有效的度量通过正则变换。由此产生的EOB哈密顿量是广义相对论哈密顿量的修改，并且已经在3 PN阶，它必须考虑非局域时间尾的贡献。我们包括后者超越圆形轨道和六阶的二进制的轨道偏心率。最后，我们计算了在平移对称ESGB模型下的双黑洞最内层稳定圆轨道（ISCO）的轨道频率。我们的工作扩展了F.L. Juli\'e和N. Deruelle [Phys. Rev. D 95，124054（2017）]，这是超越广义相对论的引力波形精确建模的重要一步。
We build an effective-one-body (EOB) Hamiltonian at third post-Newtonian (3PN) order in scalar-tensor (ST) and Einstein-scalar-Gauss-Bonnet (ESGB) theories of gravity. The latter is an extension of general relativity that predicts scalar hair for black holes. We start from the known two-body Lagrangian at 3PN order, and use order-reduction methods to construct its ordinary Hamiltonian counterpart. We then reduce the conservative two-body dynamics to the (nongeodesic) motion of a test particle in an effective metric by means of canonical transformations. The resulting EOB Hamiltonian is a modification of the general relativistic Hamiltonian, and already at 3PN order, it must account for nonlocal-in-time tail contributions. We include the latter beyond circular orbits and up to sixth order in the binary's orbital eccentricity. We finally calculate the orbital frequency at the innermost stable circular orbit (ISCO) of binary black holes in the shift-symmetric ESGB model. Our work extends F.L. Juli\'e and N. Deruelle [Phys. Rev. D 95, 124054 (2017)], and it is an essential step toward the accurate modeling of gravitational waveforms beyond general relativity.