标题： 高阶导数爱因斯坦-Æther 黑洞附近周期运动的引力波特征 显示英文标题

标题： Gravitational Wave Signatures of Periodic Motion near Higher-Derivative Einstein-Æther Black Holes

摘要： 广义相对论的高阶导数修正通常从量子引力的有效场论方法中预期，它们在如爱因斯坦-以太理论这样的洛伦兹破缺理论中自然出现。 在本工作中，我们研究了在二次曲率修正补充下的爱因斯坦-以太理论中的黑洞时空，包括与$R^2$、$R_{\mu\nu} R^{\mu\nu}$和$R_{\mu\nu\lambda\rho} R^{\mu\nu\lambda\rho}$成正比的项。 我们微扰地推导了修正后的静态、球对称度规，并检查了其对测地线结构和引力波辐射的影响。 特别是，我们分析了该背景中的周期性类时轨道，并使用四极近似计算了相关的张量模引力波形。 我们的结果表明，即使是很小的高阶导数修正也能在轨道动力学中引起可区分的偏移，并在引力波信号中留下特征相位调制和谐波变形。 这些效应以对耦合常数$\alpha$、$\beta$和$\gamma$以及以太参数$c_{13}$敏感的方式修改$h_{+}$和$h_{\times}$的频率谱和振幅包络。 这些结果特征提供了观察广义相对论和强场区域中洛伦兹对称性在紫外区偏离的潜在观测窗口。 显示英文摘要

摘要： Higher-derivative modifications of general relativity are generically expected from effective field theory approaches to quantum gravity, and they arise naturally in Lorentz-violating theories such as Einstein-Ether gravity. In this work, we investigate black hole spacetimes within Einstein-Ether theory supplemented by quadratic curvature corrections, including terms proportional to $R^2$, $R_{\mu\nu} R^{\mu\nu}$, and $R_{\mu\nu\lambda\rho} R^{\mu\nu\lambda\rho}$. We derive the corrected static, spherically symmetric metric perturbatively and examine its effects on the geodesic structure and gravitational wave emission. In particular, we analyze periodic timelike orbits in this background and compute the associated tensor-mode gravitational waveforms using the quadrupole approximation. Our results demonstrate that even small higher-derivative corrections can induce distinguishable shifts in the orbital dynamics and imprint characteristic phase modulations and harmonic deformations in the gravitational wave signal. These effects modify the frequency spectrum and amplitude envelope of $h_{+}$ and $h_{\times}$ in a manner sensitive to the coupling constants $\alpha$, $\beta$, and $\gamma$, and the Ether parameter $c_{13}$. The resulting signatures provide a potential observational window into ultraviolet deviations from general relativity and Lorentz symmetry in the strong-field regime.