AI 中文总结
研究克尔-贝托蒂-罗宾逊黑洞无质量标量散射，通过特定透明边界条件和数值求解实频散射问题，揭示反射数据依赖边界规定，超辐射受双门机制控制，给出不同自旋和磁场下的相关变化情况。
AI 中文摘要
我们针对旋转的克尔-贝托蒂-罗宾逊（Kerr-BR）黑洞几何上的中性、最小耦合、无质量标量，制定并数值求解实频散射问题，在坐标端使用特定透明边界条件。由于背景麦克斯韦应力张量无迹，最小耦合波动方程简化为四维共形波动方程，通过共形因子对标量场缩放后能进行精确的类卡特分离。与渐近平坦情形不同，坐标端\(r\to\infty\)处于有限乌龟坐标距离处。我们表明所得反射数据取决于此边界规定而非定义唯一、与观测者无关的截面。在透明端模型中，开放通道超辐射由双门机制控制，需要局部视界条件和外部传播条件\(q_\infty^2>0\)。在基准自旋\(a/M = 0.9\)时，同向旋转偶极放大随外部磁场增加而减小。关键在于，磁场在\(BM\simeq0.243\)时使开放超辐射窗口变窄并关闭。在传播阈值附近，放大系数随外部波数线性消失。
英文摘要
We formulate and numerically solve the real-frequency scattering problem for a neutral, minimally coupled, massless scalar on the rotating Kerr--Bertotti--Robinson (Kerr--BR) black-hole geometry, using a specified transparent boundary condition at the coordinate end. Since the Maxwell stress tensor of the background is traceless, the minimally coupled wave equation reduces to the four-dimensional conformal wave equation, enabling exact Carter-like separation after scaling the scalar field by the conformal factor. Unlike the asymptotically flat case, the coordinate end $r\to\infty$ lies at a finite tortoise distance. We show that the resulting reflection data are conditional on this boundary prescription rather than defining a unique, observer-independent cross section. Within the transparent-end model,open-channel superradiance is governed by a double-gate mechanism requiring both the local horizon condition and the outer propagation condition $q_\infty^2>0$. At the benchmark spin $a/M=0.9$, the co-rotating dipole amplification decreases as the external magnetic field increases. Crucially, the field narrows and closes the open superradiant window at $BM\simeq0.243$. Near the propagation threshold, the amplification coefficient vanishes linearly with the outer wave number.
