AI 中文总结
研究霍拉瓦-里夫希茨引力中引力波传播，通过构建修正波算子的推迟格林函数等方法，得到辐射区波形及相关物理量，应用于双黑洞系统，还根据观测频率得出修正及系数范围。
AI 中文摘要
我们研究了霍拉瓦-里夫希茨引力的主导奇偶性偶数红外截断中引力波的产生和传播，其特征在于修正的张量色散关系\(\omega^{2}=k^{2}+\alpha k^{4}\)。在横向无迹扇区中，我们表明高阶空间导数修正保留了传统的加号和交叉极化，且不引入极化混合、螺旋度分裂或引力双折射。我们构建了修正波算子的推迟格林函数，并推导了辐射区波形至\(\alpha\)的一阶。所得信号呈现出频率依赖的振幅重整化以及在源-观测者距离上累积的色散传播相位。我们将该形式体系应用于准圆形轨道的双黑洞系统，得到任意观测方向的极化波形。我们进一步推导了相应的能量通量、总光度和绝热啁啾演化。根据观测到的引力波频率\(f\)，主导修正满足\(\Delta h_{A}/h_{A}^{\mathrm{GR}}=-8\pi^{2}\alpha f^{2}\)和\(\Delta P/P_{\mathrm{GR}} =\Delta\dot{f}/\dot{f}_{\mathrm{GR}} =-16\pi^{2}\alpha f^{2}\)，而累积的产生相位具有相对第三后牛顿贡献的频率依赖性。通过将霍拉瓦-里夫希茨系数映射到LIGO-Virgo-KAGRA修正色散参数化，我们从GWTC - 4.0后验中在90%可信度下得到\(-6.2\times10^{2}\,\mathrm{eV}^{-2} <\alpha< 1.9\times10^{2}\,\mathrm{eV}^{-2}\)。
英文摘要
We investigate the generation and propagation of gravitational waves in the leading parity-even infrared truncation of Hořava-Lifshitz gravity, characterized by the modified tensor dispersion relation $ω^{2}=k^{2}+αk^{4}$. Working in the transverse-traceless sector, we show that the higher-spatial-derivative correction preserves the conventional plus and cross polarizations and introduces neither polarization mixing, helicity splitting, nor gravitational birefringence. We construct the retarded Green function of the modified wave operator and derive the radiation-zone waveform to first order in $α$. The resulting signal exhibits a frequency-dependent amplitude renormalization together with a dispersive propagation phase that accumulates over the source-observer distance. We apply the formalism to a binary black hole system in a quasi-circular orbit and obtain the polarization waveforms for an arbitrary observation direction. We further derive the corresponding energy flux, total luminosity, and adiabatic chirp evolution. In terms of the observed gravitational wave frequency $f$, the leading corrections satisfy $Δh_{A}/h_{A}^{\mathrm{GR}}=-8π^{2}αf^{2}$ and $ΔP/P_{\mathrm{GR}} =Δ\dot{f}/\dot{f}_{\mathrm{GR}} =-16π^{2}αf^{2}$, while the accumulated generation phase has the frequency dependence of a relative third post-Newtonian contribution. By mapping the Hořava-Lifshitz coefficient to the LIGO-Virgo-KAGRA modified-dispersion parametrization, we obtain $-6.2\times10^{2}\,\mathrm{eV}^{-2} <α< 1.9\times10^{2}\,\mathrm{eV}^{-2}$ at $90\%$ credibility from the GWTC-4.0 posterior.
Comments35 pages and 6 figures. Suggestions (about contents or refs) are welcome
