Electromagnetic observations of the radiation emitted by an accretion disk around a black hole, as well as gravitational wave observations of coalescing binaries, can be used to probe strong-field gravity. We here compare the constraints that these two types of observations can impose on theory-agnostic, parametric deviations from the Schwarzschild metric. On the gravitational wave side, we begin by computing the leading-order deviation to the Hamiltonian of a binary system in a quasi-circular orbit within the post-Newtonian approximation, given a parametric deformation of the Schwarzschild metrics of each binary component. We then compute the leading-order deviation to the gravitational waves emitted by such a binary in the frequency domain, assuming purely Einsteinian radiation-reaction. We compare this model to the LIGO-Virgo collaboration gravitational wave detections and place constraints on the metric deformation parameters, concluding with an estimate of the constraining power of aLIGO at design sensitivity. On the electromagnetic side, we first simulate observations with current and future X-ray instruments of an X-ray binary with a parametrically-deformed Schwarzschild black hole, and we then estimate constraints on the deformation parameters using these observations.We find that current gravitational wave observations have already placed constraints on the metric deformation parameters than are slightly more stringent than what can be achieved with current X-ray instruments. Moreover, future gravitational wave observations with aLIGO at design sensitivity by 2026 will be even more stringent, becoming stronger than constraints achievable with future ATHENA X-ray observations before it flies in 2034.

中文翻译：

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强场重力的引力波与 X 射线测试

黑洞周围吸积盘发出的辐射的电磁观测，以及聚结双星的引力波观测，可用于探测强场引力。我们在这里比较了这两种类型的观察可以对与 Schwarzschild 度量的理论无关的参数偏差施加的约束。在引力波方面，我们首先在后牛顿近似内的准圆形轨道中计算二元系统哈密顿量的前级偏差，假设每个二元分量的 Schwarzschild 度量的参数变形。然后，假设纯粹是爱因斯坦辐射反应，我们在频域中计算这种双星发射的引力波的前级偏差。我们将该模型与 LIGO-Virgo 协作引力波探测进行比较，并对度量变形参数施加约束，最后估计 aLIGO 在设计灵敏度下的约束能力。在电磁方面，我们首先用当前和未来的 X 射线仪器模拟具有参数变形的 Schwarzschild 黑洞的 X 射线双星的观测，然后我们使用这些观测估计变形参数的约束。我们发现当前的引力波观测已经对公制变形参数施加了限制，比目前的 X 射线仪器所能达到的要严格一些。此外，到 2026 年，在设计灵敏度下使用 aLIGO 进行的未来引力波观测将更加严格，