AI 中文总结
该研究利用EMRI对克尔动力学偏离的敏感性，构建旋转加速黑洞的EMRI波形计算框架，发现弱加速度可在长时标EMRI上产生量级为弧度的相位印记。
AI 中文摘要
极端质量比旋近（EMRI）可将克尔动力学的微小偏离放大为在多个轨道周期内累积的显著引力波相位偏移。我们利用这种敏感性研究旋转黑洞的加速度对EMRI波形的印记。自旋C度规对标准克尔通量框架构成两个障碍：时空非渐近平坦，且加速度破坏了支持严格赤道类时圆轨道的反射对称性。对于足够小的加速度AM，我们因此在满足M/r≪1和Ar≪1的类克尔中间波区中构建计算方案，通过检验耦合径向-极向稳定性构造近赤道圆轨道。我们推导自旋-2径向Teukolsky方程的分离点粒子源，构造正则归一化角向解，利用Sasaki-Nakamura变换和格林函数方法求解径向方程，并将所得的视界与远区通量耦合到稳定近赤道圆轨道的绝热演化。该框架可恢复克尔极限，且以10^-7量级的相对误差重现主导l=2克尔通量。加速度同时改变辐射反作用和轨道频率，产生特征性非单调累积相位偏移。对于M=10^6M⊙、ms/M=10^-5、a/M=0.7和AM=3×10^-7的情况，主导模式的相位偏移在一年内略超过1弧度。因此，在当前近似的可控范围内，即使弱加速度也能在长时标EMRI上产生量级为弧度的长期相位印记。
英文摘要
Extreme mass-ratio inspirals (EMRIs) can magnify small departures from Kerr dynamics into appreciable gravitational-wave phase shifts accumulated over many orbital cycles. We exploit this sensitivity to investigate the imprint of a rotating black hole's acceleration on an EMRI waveform. The spinning C metric poses two obstacles to the standard Kerr flux framework: the spacetime is not asymptotically flat, and the acceleration breaks the reflection symmetry that supports exactly equatorial circular timelike orbits. For sufficiently small acceleration $AM$, we therefore formulate the calculation in an intermediate Kerr-like wave zone satisfying $M/r\ll1$ and $Ar\ll1$, and construct a near-equatorial circular orbit by examining its coupled radial--polar stability. We derive the separated point-particle source for the spin$-2$ radial Teukolsky equation, construct a regular normalized angular solution, solve the radial equation using the Sasaki--Nakamura transformation and the Green function method, and couple the resulting horizon and far-zone fluxes to the adiabatic evolution of stable near-equatorial circular orbits. The framework recovers the Kerr limit and reproduces the dominant $l=2$ Kerr fluxes with relative errors of order $10^{-7}$. Acceleration modifies both radiation reaction and the orbital frequency, producing a characteristic nonmonotonic accumulated dephasing. For $M=10^6M_\odot$, $m_s/M=10^{-5}$, $a/M=0.7$, and $AM=3\times10^{-7}$, the dominant-mode dephasing slightly exceeds $1$ rad over one year. Thus even weak acceleration can generate an order-radian secular phase imprint on long-duration EMRIs within the controlled regime of the present approximation.
Comments19 pages, 5 figures, 1 table
