Pöschl-Teller势的Green函数
Green function of the Pöschl-Teller potential
AI总结：
本文利用Pöschl-Teller近似势精确求解黑洞微扰时域Green函数，揭示早期指数增长模式、波形的瞬时与历史分解，并证明其在红移频率处无零极点。
摘要：
我们采用Regge-Wheeler-Zerilli势的一种近似（称为Pöschl-Teller势），在考虑所有因果性条件的情况下，精确计算了这一简化模型中黑洞微扰的时域Green函数。我们发现Green函数中存在一个额外的早期时间段，它在信号与势垒最高点相互作用之前贡献出新的指数增长模式。波形本身被分解为恰沿Green函数光锥传播的瞬时部分，以及依赖于系统在光锥内过去轨迹的历史部分。我们还研究了红移模式，并证明Regge-Wheeler-Zerilli Green函数在其频率处是正则的，既没有零点也没有极点。
英文摘要：
We use an approximation of the Regge-Wheeler-Zerilli potential, known as Pöschl-Teller, to exactly compute the time-domain Green function of black hole perturbations in this simplified model, taking into account all causality conditions. We find the existence of an additional early times piece in the Green function, contributing to new exponentially growing modes just before the signal interacts with the maximum of the potential. The waveform itself is decomposed as an instantaneous piece traveling exactly on the light-cones of the Green function and a historical piece depending on the past trajectory of the system inside the light-cone. We also study redshift modes and show that the Regge-Wheeler-Zerilli Green function is regular at their frequency, with no zero nor pole.
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