AI 中文总结
该研究采用后牛顿近似，首次计算大质量标量高斯-博内引力中无自旋黑洞双天体系统的动力学，得到相关轨道解与束缚能，发现标量质量修正对高偏心率、高比质量系统影响显著，可为引力波计算提供基础。
AI 中文摘要
致密天体的旋近双天体系统可探测强场区域的引力，进而探索广义相对论的高阶曲率修正。宇称不变的二次修正可由标量高斯-博内（sGB）理论描述，该理论包含与曲率标量动态耦合的标量场，可在黑洞周围产生标量凝聚。考虑标量场的质量是自然的，会产生与该额外尺度相关的新现象学。我们采用后牛顿（PN）近似计算大质量sGB中无自旋黑洞双天体系统的动力学，得到圆轨道和椭圆轨道下的运动方程、质心变换及束缚能的解，精度达1PN阶，首次纳入高阶曲率与标量质量的耦合修正。我们的大部分计算适用于任意标量质量，最终显式表达式假设标量质量远小于双天体总质量，并按该比值展开至二阶。研究表明，规范不变束缚能的标量质量修正带有同阶与异阶项，在微扰极限下贡献整体异号，使束缚能略有减小；该效应对高质量比、大偏心率的双天体系统最为显著。我们的方法和结果也可作为计算此类系统引力波的基础。
英文摘要
Inspiraling binary systems of compact objects probe gravity in strong-field regimes, thereby exploring potential higher curvature corrections to General Relativity. Parity-invariant quadratic corrections can be described by scalar-Gauss-Bonnet (sGB) theory, which involves a scalar field dynamically coupled to curvature scalars and can give rise to scalar condensates around black holes. Considering a mass for the scalar field is natural and leads to new phenomenology related to this additional scale. We compute the dynamics of a binary system of nonspinning black holes in massive sGB using the post-Newtonian (PN) approximation. We obtain solutions for the equations of motion, center-of-mass transformation, and binding energy for circular and eccentric orbits up to 1PN order, where for the first time the higher curvature coupled to scalar mass corrections are included. While most of our calculations are valid for generic scalar masses, the final explicit expressions assume that the mass is small compared to the total mass of the binary and expand to quadratic order in this ratio. We show that the scalar mass corrections to the gauge-invariant binding energy come with same and opposite sign order terms, contributing an overall opposite sign contribution in the perturbative limit, decreasing the binding energy slightly. The effects are largest for binary systems with high mass ratio and large eccentricity. Our methods and results will also be useful as a basis for computing the gravitational waves sourced by such systems.
Comments32 pages + appendix, 7 figures
