论文标题
纽顿后第三次有效的哈密顿量在标量张量和爱因斯坦 - 斯卡尔 - 高斯 - 邦网重力中
Third post-Newtonian effective-one-body Hamiltonian in scalar-tensor and Einstein-scalar-Gauss-Bonnet gravity
论文作者
论文摘要
我们在标量调整器（ST）和Einstein-Scalar-Gauss-Bonnet（ESGB）重力理论中建立了一个有效的汉密尔顿（EOB）哈密顿量。后者是一般相对论的扩展，可预测黑洞的标量头发。我们以3pn顺序从已知的两体Lagrangian开始，并使用订购方法来构建其普通的汉密尔顿对应物。然后，我们通过规范转换将保守的两体动力学减少到有效度量标准中测试粒子的（非晶状体）运动。由此产生的EOB Hamiltonian是对一般相对论的哈密顿量的修改，并且已经以3pn的顺序来说明了非局限性的尾巴贡献。我们包括后者以外的圆形轨道，最多可在二进制轨道偏心率中进行第六阶。我们最终在移位对称ESGB模型中的二进制黑洞的最内向圆形轨道（ISCO）处计算轨道频率。我们的工作扩展了F.L. Julié和N. Deruelle [Phys。 Rev. D 95，124054（2017）]，这是朝着超出一般相对性的重力波形进行准确建模的重要步骤。
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. Julié 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.
